Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: getFFTI

type_of(data) :: fft(1 : getExpNext(size(data)))

fft(:) = getFFTI(data(:))

pm_fftnr::getFFTI
Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequen...
Definition: pm_fftnr.F90:428

pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftnr, only: getFFTF, getFFTI

6 use pm_distUnif, only: getUnifRand

7 use pm_mathCompare, only: isClose

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: i

13 integer(IK) :: lenData

14 type(display_type) :: disp

15 disp = display_type(file = "main.out.F90")

16

17 do i = 1, 5

18 block

19 use pm_kind, only: TKC => CKS

20 real(TKC) :: reltol

21 complex(TKC), allocatable :: data(:), atad(:)

22 call disp%show("lenData = getUnifRand(5, 100)")

23 lenData = getUnifRand(5, 100)

24 call disp%show("lenData")

25 call disp%show( lenData )

26 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

27 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

28 call disp%show("data")

29 call disp%show( data )

30 call disp%skip()

31 call disp%show("atad = getFFTI(getFFTF(data))")

32 atad = getFFTI(getFFTF(data))

33 call disp%show("atad")

34 call disp%show( atad )

35 call disp%show("reltol = sqrt(epsilon(1._TKC))")

36 reltol = sqrt(epsilon(1._TKC))

37 call disp%show("reltol")

38 call disp%show( reltol )

39 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

40 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

41 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

42 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKC => CKD

48 real(TKC) :: reltol

49 complex(TKC), allocatable :: data(:), atad(:)

50 call disp%show("lenData = getUnifRand(5, 100)")

51 lenData = getUnifRand(5, 100)

52 call disp%show("lenData")

53 call disp%show( lenData )

54 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

55 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

56 call disp%show("data")

57 call disp%show( data )

58 call disp%skip()

59 call disp%show("atad = getFFTI(getFFTF(data))")

60 atad = getFFTI(getFFTF(data))

61 call disp%show("atad")

62 call disp%show( atad )

63 call disp%show("reltol = sqrt(epsilon(1._TKC))")

64 reltol = sqrt(epsilon(1._TKC))

65 call disp%show("reltol")

66 call disp%show( reltol )

67 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

68 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

69 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

70 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

71 call disp%skip()

72 end block

73

74 block

75 use pm_kind, only: TKC => CKH

76 real(TKC) :: reltol

77 complex(TKC), allocatable :: data(:), atad(:)

78 call disp%show("lenData = getUnifRand(5, 100)")

79 lenData = getUnifRand(5, 100)

80 call disp%show("lenData")

81 call disp%show( lenData )

82 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

83 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

84 call disp%show("data")

85 call disp%show( data )

86 call disp%skip()

87 call disp%show("atad = getFFTI(getFFTF(data))")

88 atad = getFFTI(getFFTF(data))

89 call disp%show("atad")

90 call disp%show( atad )

91 call disp%show("reltol = sqrt(epsilon(1._TKC))")

92 reltol = sqrt(epsilon(1._TKC))

93 call disp%show("reltol")

94 call disp%show( reltol )

95 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

96 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

97 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

98 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

99 call disp%skip()

100 end block

101

102 block

103 use pm_kind, only: TKC => RKS

104 real(TKC) :: reltol

105 real(TKC), allocatable :: data(:), atad(:)

106 call disp%show("lenData = getUnifRand(5, 100)")

107 lenData = getUnifRand(5, 100)

108 call disp%show("lenData")

109 call disp%show( lenData )

110 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

111 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

112 call disp%show("data")

113 call disp%show( data )

114 call disp%skip()

115 call disp%show("atad = getFFTI(getFFTF(data))")

116 atad = getFFTI(getFFTF(data))

117 call disp%show("atad")

118 call disp%show( atad )

119 call disp%show("reltol = sqrt(epsilon(1._TKC))")

120 reltol = sqrt(epsilon(1._TKC))

121 call disp%show("reltol")

122 call disp%show( reltol )

123 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

124 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

125 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

126 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: TKC => RKD

132 real(TKC) :: reltol

133 real(TKC), allocatable :: data(:), atad(:)

134 call disp%show("lenData = getUnifRand(5, 100)")

135 lenData = getUnifRand(5, 100)

136 call disp%show("lenData")

137 call disp%show( lenData )

138 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

139 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

140 call disp%show("data")

141 call disp%show( data )

142 call disp%skip()

143 call disp%show("atad = getFFTI(getFFTF(data))")

144 atad = getFFTI(getFFTF(data))

145 call disp%show("atad")

146 call disp%show( atad )

147 call disp%show("reltol = sqrt(epsilon(1._TKC))")

148 reltol = sqrt(epsilon(1._TKC))

149 call disp%show("reltol")

150 call disp%show( reltol )

151 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

152 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

153 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

154 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKC => RKH

160 real(TKC) :: reltol

161 real(TKC), allocatable :: data(:), atad(:)

162 call disp%show("lenData = getUnifRand(5, 100)")

163 lenData = getUnifRand(5, 100)

164 call disp%show("lenData")

165 call disp%show( lenData )

166 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

167 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

168 call disp%show("data")

169 call disp%show( data )

170 call disp%skip()

171 call disp%show("atad = getFFTI(getFFTF(data))")

172 atad = getFFTI(getFFTF(data))

173 call disp%show("atad")

174 call disp%show( atad )

175 call disp%show("reltol = sqrt(epsilon(1._TKC))")

176 reltol = sqrt(epsilon(1._TKC))

177 call disp%show("reltol")

178 call disp%show( reltol )

179 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

180 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

181 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

182 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

183 call disp%skip()

184 end block

185 end do

186

187end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4106

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11074

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:523

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:10962

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:28

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:281

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:477

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:310

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:280

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:311

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:308

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:279

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind a...
Definition: pm_kind.F90:462

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:307

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10228

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_intel* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte_fortran_*_intel*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_gnu* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+81

4data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

5data

6(+1.04480124, +0.523545742E-1), (+1.69275928, +0.985900521), (+1.63477325, +0.340221167), (+1.56278014, +0.692016363), (+1.62734449, +0.371844113), (+1.35602283, +0.894298971), (+1.54629636, +0.413004756E-1), (+1.01187503, +0.377765596), (+1.22818530, +0.749990821), (+1.77054024, +0.594566464E-1), (+1.32179081, +0.247484744), (+1.21237278, +0.279776752), (+1.75127697, +0.814414680), (+1.74804521, +0.467378497), (+1.83173919, +0.452116668), (+1.38609099, +0.661826074), (+1.84712768, +0.423899412), (+1.84845066, +0.126201987), (+1.06628156, +0.491264760), (+1.83184791, +0.337892115), (+1.97141886, +0.905144453), (+1.92322516, +0.797132432), (+1.77096212, +0.152186275), (+1.03956497, +0.924317181), (+1.95744610, +0.733123124), (+1.82301474, +0.126960158), (+1.54140151, +0.612691522), (+1.30476475, +0.440519452), (+1.87468827, +0.558859527), (+1.18365884, +0.751362026), (+1.93607235, +0.922337413), (+1.85073829, +0.227919281), (+1.67753577, +0.331558287), (+1.63511944, +0.655454576), (+1.95050287, +0.914514065), (+1.41259754, +0.961841762), (+1.89469624, +0.835870385), (+1.23098350, +0.168221772), (+1.04250789, +0.401091576E-2), (+1.09131551, +0.212076962), (+1.84871268, +0.868723333), (+1.82350063, +0.771769881), (+1.98827720, +0.511461973), (+1.30449557, +0.392072558), (+1.88980961, +0.582757115), (+1.33792567, +0.570987284), (+1.64491546, +0.431108534), (+1.78114736, +0.607664406), (+1.23068976, +0.822140872), (+1.41708660, +0.461014271), (+1.85174596, +0.849517047), (+1.45704913, +0.318162441E-1), (+1.25950968, +0.530031204), (+1.06345654, +0.286446273), (+1.27265477, +0.712803364), (+1.35850143, +0.726630449), (+1.64143074, +0.408601165E-1), (+1.23923099, +0.616242647), (+1.97835875, +0.110600710), (+1.41862142, +0.691992342), (+1.09774518, +0.334343910E-1), (+1.21554244, +0.123366475), (+1.41987062, +0.724963069), (+1.68035364, +0.353772640), (+1.44335413, +0.149697602), (+1.12732625, +0.267398298), (+1.23663986, +0.469513535E-1), (+1.26960182, +0.564499855), (+1.41766298, +0.450728238), (+1.50736630, +0.955280542), (+1.27632105, +0.822333395), (+1.44273067, +0.239107668), (+1.36831141, +0.592969239), (+1.23967314, +0.786994338), (+1.70833707, +0.842767894), (+1.01370573, +0.706738830E-1), (+1.01424074, +0.179655254), (+1.56741261, +0.804989457), (+1.77274311, +0.487046421), (+1.57565379, +0.146943331E-2), (+1.63895774, +0.305056095)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.04480124, +0.523545444E-1), (+1.69275928, +0.985900640), (+1.63477290, +0.340221405), (+1.56278014, +0.692016244), (+1.62734437, +0.371843904), (+1.35602272, +0.894298851), (+1.54629600, +0.413002670E-1), (+1.01187491, +0.377765417), (+1.22818542, +0.749990702), (+1.77054036, +0.594567955E-1), (+1.32179081, +0.247484744), (+1.21237290, +0.279776841), (+1.75127709, +0.814414561), (+1.74804509, +0.467378616), (+1.83173907, +0.452116609), (+1.38609099, +0.661825895), (+1.84712756, +0.423899442), (+1.84845066, +0.126202211), (+1.06628132, +0.491264790), (+1.83184779, +0.337892056), (+1.97141862, +0.905144334), (+1.92322493, +0.797132492), (+1.77096164, +0.152186215), (+1.03956485, +0.924317002), (+1.95744598, +0.733123183), (+1.82301486, +0.126960471), (+1.54140139, +0.612691402), (+1.30476487, +0.440519691), (+1.87468827, +0.558859587), (+1.18365884, +0.751361966), (+1.93607235, +0.922337413), (+1.85073817, +0.227919400), (+1.67753577, +0.331558049), (+1.63511944, +0.655454516), (+1.95050287, +0.914513588), (+1.41259778, +0.961841702), (+1.89469647, +0.835870087), (+1.23098350, +0.168221608), (+1.04250789, +0.401081145E-2), (+1.09131563, +0.212076932), (+1.84871268, +0.868723273), (+1.82350063, +0.771769881), (+1.98827696, +0.511461735), (+1.30449557, +0.392072499), (+1.88980961, +0.582757115), (+1.33792591, +0.570987225), (+1.64491534, +0.431108236), (+1.78114736, +0.607664227), (+1.23068953, +0.822140694), (+1.41708648, +0.461014092), (+1.85174561, +0.849516630), (+1.45704889, +0.318160951E-1), (+1.25950968, +0.530031085), (+1.06345654, +0.286446214), (+1.27265477, +0.712803006), (+1.35850132, +0.726630211), (+1.64143062, +0.408601910E-1), (+1.23923075, +0.616242528), (+1.97835851, +0.110600665), (+1.41862130, +0.691992283), (+1.09774530, +0.334343985E-1), (+1.21554244, +0.123366430), (+1.41987050, +0.724962652), (+1.68035328, +0.353772432), (+1.44335413, +0.149697572), (+1.12732625, +0.267398208), (+1.23663986, +0.469511300E-1), (+1.26960206, +0.564499855), (+1.41766310, +0.450728208), (+1.50736630, +0.955280364), (+1.27632105, +0.822333217), (+1.44273067, +0.239107624), (+1.36831117, +0.592969418), (+1.23967278, +0.786994338), (+1.70833695, +0.842767894), (+1.01370585, +0.706739798E-1), (+1.01424062, +0.179655433), (+1.56741226, +0.804989696), (+1.77274311, +0.487046361), (+1.57565379, +0.146940351E-2), (+1.63895738, +0.305056125), (-0.596046448E-7, -0.193715096E-6), (+0.417232513E-6, -0.298023224E-7), (+0.238418579E-6, +0.00000000), (+0.596046448E-7, -0.894069672E-7), (+0.00000000, +0.149011612E-6), (+0.357627869E-6, +0.178813934E-6), (+0.298023224E-6, +0.119209290E-6), (+0.00000000, -0.238418579E-6), (-0.238418579E-6, -0.253319740E-6), (+0.596046448E-7, -0.149011612E-6), (+0.238418579E-6, -0.745058060E-7), (-0.119209290E-6, -0.119209290E-6), (-0.596046448E-7, -0.298023224E-7), (+0.00000000, -0.894069672E-7), (+0.00000000, -0.171363354E-6), (-0.596046448E-7, +0.447034836E-7), (-0.596046448E-7, +0.149011612E-6), (+0.00000000, +0.268220901E-6), (+0.00000000, +0.268220901E-6), (+0.00000000, +0.178813934E-6), (+0.596046448E-7, +0.223517418E-6), (+0.178813934E-6, +0.283122063E-6), (+0.119209290E-6, +0.178813934E-6), (+0.596046448E-7, +0.298023224E-7), (-0.238418579E-6, -0.894069672E-7), (+0.178813934E-6, +0.268220901E-6), (+0.178813934E-6, +0.447034836E-7), (+0.00000000, -0.298023224E-7), (-0.596046448E-7, +0.00000000), (+0.238418579E-6, +0.193715096E-6), (+0.119209290E-6, +0.298023224E-7), (-0.596046448E-7, +0.298023224E-7), (+0.00000000, +0.134110451E-6), (+0.178813934E-6, +0.447034836E-6), (+0.298023224E-6, +0.298023224E-7), (+0.00000000, +0.178813934E-6), (+0.00000000, +0.298023224E-7), (+0.596046448E-7, +0.357627869E-6), (+0.119209290E-6, +0.238418579E-6), (+0.298023224E-6, -0.104308128E-6), (+0.238418579E-6, -0.208616257E-6), (+0.298023224E-6, +0.134110451E-6), (+0.417232513E-6, -0.298023224E-7), (+0.119209290E-6, -0.968575478E-7), (+0.00000000, -0.447034836E-7), (+0.119209290E-6, +0.238418579E-6), (+0.238418579E-6, +0.894069672E-7)

11reltol = sqrt(epsilon(1._TKC))

12reltol

13+0.345266977E-3

14isClose(data, atad(1:size(data)), reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+21

21data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

22data

23(+1.4945080279405960, +0.28239652174047369), (+1.4986058896076155, +0.43926796786528011), (+1.1112620937527873, +0.99777954445722494), (+1.3238754675691249, +0.64112100151852081), (+1.3612462135260430, +0.49530541530958216), (+1.0273046133476693, +0.43119640944798032), (+1.6534219084377051, +0.79872808215311619), (+1.1101974076731493, +0.33095548842044142), (+1.5999803409031730, +0.81599148984539749), (+1.6852793708628009, +0.74253692913084091), (+1.4631290955281022, +0.40606674356908345E-1), (+1.8346636991009095, +0.97867532763089449), (+1.2777423442370734, +0.62250754376727302), (+1.8202450400183636, +0.49383900120144375E-1), (+1.9782101999564956, +0.96521297548939544), (+1.2785838440285811, +0.59330775708016059), (+1.2067849983638717, +0.85026057803986310E-2), (+1.6288682516757678, +0.56153750018850856), (+1.0303962040617864, +0.16567998840626830), (+1.1000458798244064, +0.25480413206918529), (+1.6867984180892237, +0.20069486469316378)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.4945080279405960, +0.28239652174047375), (+1.4986058896076151, +0.43926796786528033), (+1.1112620937527871, +0.99777954445722505), (+1.3238754675691242, +0.64112100151852092), (+1.3612462135260430, +0.49530541530958228), (+1.0273046133476691, +0.43119640944798054), (+1.6534219084377044, +0.79872808215311619), (+1.1101974076731489, +0.33095548842044170), (+1.5999803409031728, +0.81599148984539727), (+1.6852793708628004, +0.74253692913084102), (+1.4631290955281018, +0.40606674356908401E-1), (+1.8346636991009089, +0.97867532763089438), (+1.2777423442370734, +0.62250754376727269), (+1.8202450400183630, +0.49383900120144125E-1), (+1.9782101999564952, +0.96521297548939511), (+1.2785838440285808, +0.59330775708016015), (+1.2067849983638717, +0.85026057803985755E-2), (+1.6288682516757675, +0.56153750018850845), (+1.0303962040617864, +0.16567998840626824), (+1.1000458798244062, +0.25480413206918517), (+1.6867984180892237, +0.20069486469316369), (+0.33306690738754696E-15, -0.27755575615628914E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.44408920985006262E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.0000000000000000, +0.55511151231257827E-16), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.27755575615628914E-15), (+0.66613381477509392E-15, +0.41633363423443370E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15)

28reltol = sqrt(epsilon(1._TKC))

29reltol

30+0.14901161193847656E-7

31isClose(data, atad(1:size(data)), reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+67

38data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

39data

40(+1.86571933161677444103692730674249836, +0.373415403872511207312391577795441996), (+1.42454874868102313296612103388753318, +0.120436083420487722849029413784614296), (+1.67644693089416593497277630161923050, +0.197786512850104508098374215372884394), (+1.21501650545015723697646184476379718, +0.588676529919953978857809279517861999), (+1.73027023565071069443103231852641613, +0.300261897768824316526749698439848376), (+1.36309500025873929965122196412617665, +0.703563383947592470597049970655615430), (+1.55899796908826006564314164027705840, +0.224854768218845129295846286717113272), (+1.40466008963552943452655807499426880, +0.847302838565618549358522743945533695), (+1.15733102843707150540849215915810721, +0.909071930277459954103120467190873519E-1), (+1.04048934420949735430973174879228146, +0.615009338737254609517416367620150392), (+1.73534452171086172692039577435238135, +0.868745055995317970414009245026860196), (+1.67879640582527817484279900087566832, +0.299950496924904211357413101227914753), (+1.04206091882401756837267738835033676, +0.432472107821069539654809222269382808), (+1.65530418131351887436717420764813005, +0.589016906413076272681684697477379786), (+1.65071402852700561152288414231046208, +0.755655303216582013770513275876108756), (+1.05347328455809287434223170921388490, +0.126717704711479203964788061093703153), (+1.85782001624096274662971324819908045, +0.927623374240171377282656595260661310), (+1.18978271747486938181682797000180374, +0.171506770296006400929517919290652554), (+1.52311138069744829337392080126255607, +0.195096367956151952167981470121953828), (+1.98570847116584758260358956540890697, +0.648416313057438119795327056744978363), (+1.06935917664395747248395440087551226, +0.326625083937413403281287091973172532), (+1.49090438594374226175393831763457880, +0.182323762218999349476859891195477311), (+1.54296714958946718906761469217671510, +0.808649555296307465475714448651745713), (+1.63700874575149669303113900400650289, +0.211161023963820768286931374105092380), (+1.90092774623073300057233480480304069, +0.503797220874371586244257066170719609), (+1.12470234341398082035605812137846042, +0.738082058287421197980405360303498084), (+1.89684262922356020983715874255822910, +0.588617220208277856096956930288895738), (+1.47602724900562206195884406913260184, +0.728898612309374163026507178982119552), (+1.46207453736752966546635707296959102, +0.126459867948486402655758846789204514), (+1.01727270961162670596311218318127018, +0.387212132912058858807783055820364717), (+1.82579407146489579366574152544270422, +0.871842644058817998431934709784995589), (+1.26372887178583898840623993016504109, +0.800577668357186564349675848619128130), (+1.30038307954345038841714078415171950, +0.696239894910769679592001642791357816), (+1.41273264040951803676879750230761268, +0.649921253347123171349619620735682425), (+1.96255457186586284140338109307287148, +0.989952455006668692814205292936163137), (+1.43480412807664665190233783138542816, +0.571713684645240517761387653716090652), (+1.65309888065834937938909371328745800, +0.501379416764482988231654477406160458), (+1.45487358297878936373652073371484067, +0.839340738049988487891893366222566121), (+1.48323497161427243164139713634888932, +0.695065705972330550423599851172711547), (+1.63314451326693066406071258977933714, +0.707899991600168321706039111525141366), (+1.85806852066022638338260072977801702, +0.376575325883952334402386684687686460), (+1.11485582553693332007679638961461500, +0.419696627717669746990858041300917421), (+1.82238744708023407175981853384152912, +0.784079759441441294140461136662590807), (+1.71367727850679214462979265655315922, +0.479007078635670101091072500167487462), (+1.66322379576897308777341585544830252, +0.873967561562884435930189501366940972), (+1.79634220828815355948409668360454423, +0.101534992367479314717740291229903756), (+1.65851333785244558347117356259714628, +0.567203942025007460150191116773270431), (+1.42722713715392011731287415249254546, +0.598921713215488761317742246528485258), (+1.17569742787284562711991948933459494, +0.419514488826996429698459574270167245), (+1.45011921932299030238404935378421183, +0.120867369564273226673617351474428487), (+1.41605808637756543993368874780175457, +0.683964342621320451733616886631554983), (+1.70382387931148794292915619113320731, +0.875863373710173654803197534209702691), (+1.18209518885821398835524042830793584, +0.753002343314261130873373321460870170E-1), (+1.88662329634389146655953245618088120, +0.124310857131350740661049919754222026), (+1.05915732311890942270817275224131880, +0.451063346735940203310738734806219299), (+1.75878081292489892597795234837571857, +0.169291421917234006921638275231789910), (+1.96868379654727255844402441693088239, +0.478093110258459547540254957186086373), (+1.92249464989851250215029019457102984, +0.228936468744313811467950114111540428), (+1.54271372208479021424918199991207584, +0.804538065155540219260575168029660865), (+1.38467352916492574918577320222940445, +0.953462754554703299148738183966942298), (+1.29367418209902219405005771674249092, +0.494379626493856393298175486930721493), (+1.49524476946197218604629766259909190, +0.957422380861691790840906937984960245), (+1.46932955225951570781542298925635272, +0.739255491230084164204498265210180740E-1), (+1.34452070942283739349941939278539943, +0.375453646079223173306443769528746343), (+1.86535935965000398579423504543600608, +0.573307277337361898566318097232969585), (+1.88989676001365996270268731024949151, +0.671710041436427212521611069568136128), (+1.78136872531654183025997878947724833, +0.778085338502155707193247609544683204)

41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.86571933161677444103692730674249817, +0.373415403872511207312391577795441948), (+1.42454874868102313296612103388753337, +0.120436083420487722849029413784613766), (+1.67644693089416593497277630161923031, +0.197786512850104508098374215372884298), (+1.21501650545015723697646184476379756, +0.588676529919953978857809279517861999), (+1.73027023565071069443103231852641613, +0.300261897768824316526749698439848280), (+1.36309500025873929965122196412617684, +0.703563383947592470597049970655615238), (+1.55899796908826006564314164027705821, +0.224854768218845129295846286717113127), (+1.40466008963552943452655807499426919, +0.847302838565618549358522743945533502), (+1.15733102843707150540849215915810760, +0.909071930277459954103120467190873760E-1), (+1.04048934420949735430973174879228165, +0.615009338737254609517416367620150488), (+1.73534452171086172692039577435238192, +0.868745055995317970414009245026860196), (+1.67879640582527817484279900087566871, +0.299950496924904211357413101227914608), (+1.04206091882401756837267738835033696, +0.432472107821069539654809222269382712), (+1.65530418131351887436717420764813063, +0.589016906413076272681684697477379786), (+1.65071402852700561152288414231046246, +0.755655303216582013770513275876108852), (+1.05347328455809287434223170921388529, +0.126717704711479203964788061093702912), (+1.85782001624096274662971324819908045, +0.927623374240171377282656595260661310), (+1.18978271747486938181682797000180393, +0.171506770296006400929517919290652313), (+1.52311138069744829337392080126255626, +0.195096367956151952167981470121953732), (+1.98570847116584758260358956540890735, +0.648416313057438119795327056744978363), (+1.06935917664395747248395440087551206, +0.326625083937413403281287091973172436), (+1.49090438594374226175393831763457918, +0.182323762218999349476859891195477335), (+1.54296714958946718906761469217671510, +0.808649555296307465475714448651745713), (+1.63700874575149669303113900400650347, +0.211161023963820768286931374105091947), (+1.90092774623073300057233480480304069, +0.503797220874371586244257066170719801), (+1.12470234341398082035605812137846042, +0.738082058287421197980405360303498469), (+1.89684262922356020983715874255822910, +0.588617220208277856096956930288896123), (+1.47602724900562206195884406913260184, +0.728898612309374163026507178982119649), (+1.46207453736752966546635707296959102, +0.126459867948486402655758846789204586), (+1.01727270961162670596311218318127038, +0.387212132912058858807783055820364910), (+1.82579407146489579366574152544270461, +0.871842644058817998431934709784995878), (+1.26372887178583898840623993016504147, +0.800577668357186564349675848619128515), (+1.30038307954345038841714078415171912, +0.696239894910769679592001642791357913), (+1.41273264040951803676879750230761307, +0.649921253347123171349619620735682618), (+1.96255457186586284140338109307287148, +0.989952455006668692814205292936163426), (+1.43480412807664665190233783138542855, +0.571713684645240517761387653716090652), (+1.65309888065834937938909371328745800, +0.501379416764482988231654477406160169), (+1.45487358297878936373652073371484087, +0.839340738049988487891893366222566218), (+1.48323497161427243164139713634888951, +0.695065705972330550423599851172711836), (+1.63314451326693066406071258977933753, +0.707899991600168321706039111525141366), (+1.85806852066022638338260072977801722, +0.376575325883952334402386684687686845), (+1.11485582553693332007679638961461539, +0.419696627717669746990858041300917614), (+1.82238744708023407175981853384152912, +0.784079759441441294140461136662591289), (+1.71367727850679214462979265655315941, +0.479007078635670101091072500167487751), (+1.66322379576897308777341585544830290, +0.873967561562884435930189501366941357), (+1.79634220828815355948409668360454480, +0.101534992367479314717740291229904021), (+1.65851333785244558347117356259714667, +0.567203942025007460150191116773270816), (+1.42722713715392011731287415249254585, +0.598921713215488761317742246528485932), (+1.17569742787284562711991948933459494, +0.419514488826996429698459574270167245), (+1.45011921932299030238404935378421221, +0.120867369564273226673617351474428511), (+1.41605808637756543993368874780175496, +0.683964342621320451733616886631555175), (+1.70382387931148794292915619113320770, +0.875863373710173654803197534209702884), (+1.18209518885821398835524042830793603, +0.753002343314261130873373321460869447E-1), (+1.88662329634389146655953245618088197, +0.124310857131350740661049919754221809), (+1.05915732311890942270817275224131880, +0.451063346735940203310738734806219588), (+1.75878081292489892597795234837571895, +0.169291421917234006921638275231790006), (+1.96868379654727255844402441693088239, +0.478093110258459547540254957186086662), (+1.92249464989851250215029019457103061, +0.228936468744313811467950114111540837), (+1.54271372208479021424918199991207584, +0.804538065155540219260575168029661635), (+1.38467352916492574918577320222940445, +0.953462754554703299148738183966943068), (+1.29367418209902219405005771674249073, +0.494379626493856393298175486930721734), (+1.49524476946197218604629766259909228, +0.957422380861691790840906937984961111), (+1.46932955225951570781542298925635291, +0.739255491230084164204498265210184351E-1), (+1.34452070942283739349941939278539982, +0.375453646079223173306443769528746921), (+1.86535935965000398579423504543600589, +0.573307277337361898566318097232969585), (+1.88989676001365996270268731024949189, +0.671710041436427212521611069568136706), (+1.78136872531654183025997878947724814, +0.778085338502155707193247609544683397), (-0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33), (-0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-33), (-0.481482486096808963263994485646231830E-33, -0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (-0.481482486096808963263994485646231830E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-34), (-0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33), (-0.674075480535532548569592279904724561E-33, -0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, +0.276852429505665153876796829246583302E-33), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34), (+0.962964972193617926527988971292463659E-34, +0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, -0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, +0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-33), (-0.385185988877447170611195588516985464E-33, -0.337037740267766274284796139952362281E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.361111864572606722447995864234673872E-33), (-0.962964972193617926527988971292463659E-34, -0.312963615962925826121596415670050689E-33), (-0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33), (-0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.312963615962925826121596415670050689E-33), (-0.481482486096808963263994485646231830E-33, -0.385185988877447170611195588516985464E-33), (-0.192592994438723585305597794258492732E-33, -0.433334237487128066937595037081608647E-33), (-0.288889491658085377958396691387739098E-33, +0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, -0.270833898429455041835996898176005404E-33), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, +0.722223729145213444895991728469347744E-34), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-34), (-0.481482486096808963263994485646231830E-33, -0.240741243048404481631997242823115915E-34), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33), (-0.385185988877447170611195588516985464E-33, -0.505556610401649411427194209928543421E-33), (-0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33), (-0.288889491658085377958396691387739098E-33, -0.770371977754894341222391177033970927E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-33), (-0.385185988877447170611195588516985464E-33, -0.403241582106077506733595381728719157E-33), (-0.577778983316170755916793382775478196E-33, -0.794446102059734789385590901316282519E-33)

45reltol = sqrt(epsilon(1._TKC))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, atad(1:size(data)), reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+98

55data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

56data

57+1.40296078, +1.34922349, +1.66813636, +1.83423090, +1.04846025, +1.13616312, +1.05081773, +1.93962264, +1.23181939, +1.83019638, +1.21196628, +1.13616490, +1.91779840, +1.01466429, +1.52732253, +1.89746284, +1.97082007, +1.79096663, +1.01951492, +1.26800609, +1.92415309, +1.11500490, +1.21368051, +1.88432503, +1.31157911, +1.51176238, +1.17340839, +1.42295325, +1.42164862, +1.45184755, +1.41641164, +1.72930408, +1.28740513, +1.76931274, +1.47460341, +1.97888756, +1.80098057, +1.40154719, +1.33039880, +1.44136715, +1.47690463, +1.91407752, +1.67583656, +1.88794374, +1.66115785, +1.80784225, +1.01540565, +1.71091270, +1.63744545, +1.45337856, +1.67936957, +1.18713117, +1.93818903, +1.28105021, +1.79157937, +1.28865623, +1.81143916, +1.68020368, +1.80219686, +1.07077265, +1.13525558, +1.71558762, +1.69944882, +1.19058430, +1.87676024, +1.01144540, +1.02841973, +1.03879511, +1.40085649, +1.86135089, +1.53588772, +1.22307098, +1.24212253, +1.86172962, +1.56896257, +1.31494045, +1.34165478, +1.23994219, +1.55176735, +1.50936508, +1.50869703, +1.79415786, +1.00991416, +1.75747848, +1.34289122, +1.07063019, +1.96273422, +1.95690560, +1.44059014, +1.55918634, +1.98723269, +1.77327275, +1.49064016, +1.93048871, +1.97178388, +1.04753840, +1.43063927, +1.54851699

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.40296102, +1.34922338, +1.66813624, +1.83423090, +1.04846025, +1.13616300, +1.05081785, +1.93962240, +1.23181951, +1.83019638, +1.21196616, +1.13616526, +1.91779876, +1.01466393, +1.52732253, +1.89746273, +1.97081995, +1.79096651, +1.01951480, +1.26800632, +1.92415321, +1.11500466, +1.21368074, +1.88432503, +1.31157923, +1.51176238, +1.17340839, +1.42295337, +1.42164886, +1.45184720, +1.41641164, +1.72930396, +1.28740525, +1.76931238, +1.47460341, +1.97888744, +1.80098069, +1.40154696, +1.33039880, +1.44136691, +1.47690475, +1.91407752, +1.67583632, +1.88794351, +1.66115820, +1.80784202, +1.01540577, +1.71091259, +1.63744545, +1.45337844, +1.67936945, +1.18713093, +1.93818927, +1.28104997, +1.79157937, +1.28865623, +1.81143928, +1.68020368, +1.80219698, +1.07077265, +1.13525593, +1.71558738, +1.69944882, +1.19058418, +1.87676048, +1.01144528, +1.02841985, +1.03879499, +1.40085697, +1.86135077, +1.53588784, +1.22307086, +1.24212277, +1.86172962, +1.56896269, +1.31494057, +1.34165502, +1.23994207, +1.55176735, +1.50936496, +1.50869703, +1.79415751, +1.00991416, +1.75747848, +1.34289157, +1.07062995, +1.96273422, +1.95690560, +1.44058990, +1.55918622, +1.98723233, +1.77327275, +1.49064028, +1.93048847, +1.97178388, +1.04753840, +1.43063927, +1.54851675, +0.119209290E-6, +0.119209290E-6, +0.476837158E-6, +0.476837158E-6, +0.238418579E-6, +0.536441803E-6, +0.238418579E-6, +0.178813934E-6, -0.596046448E-7, +0.476837158E-6, +0.357627869E-6, +0.596046448E-7, +0.119209290E-6, +0.357627869E-6, +0.417232513E-6, -0.596046448E-7, +0.357627869E-6, +0.178813934E-6, +0.417232513E-6, +0.178813934E-6, +0.357627869E-6, +0.298023224E-6, +0.298023224E-6, -0.596046448E-7, +0.357627869E-6, -0.596046448E-7, +0.476837158E-6, -0.178813934E-6, +0.298023224E-6, -0.178813934E-6

62reltol = sqrt(epsilon(1._TKC))

63reltol

64+0.345266977E-3

65isClose(data, atad(1:size(data)), reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+18

72data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

73data

74+1.5895141271131448, +1.8513212180722807, +1.6123453484869159, +1.7903778020927263, +1.6113560155771953, +1.8761629088824692, +1.0201658888564986, +1.4886891393294370, +1.8526462499775915, +1.3963366440192648, +1.4822586692388162, +1.3348696194434289, +1.1717682846864093, +1.4202162360980735, +1.9345080814658535, +1.9546218387778409, +1.5525106213831656, +1.6371464950002894

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.5895141271131448, +1.8513212180722805, +1.6123453484869161, +1.7903778020927268, +1.6113560155771953, +1.8761629088824689, +1.0201658888564979, +1.4886891393294372, +1.8526462499775915, +1.3963366440192646, +1.4822586692388167, +1.3348696194434289, +1.1717682846864093, +1.4202162360980732, +1.9345080814658533, +1.9546218387778400, +1.5525106213831656, +1.6371464950002890, -0.11102230246251565E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.11102230246251565E-14

79reltol = sqrt(epsilon(1._TKC))

80reltol

81+0.14901161193847656E-7

82isClose(data, atad(1:size(data)), reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+12

89data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

90data

91+1.69128244610153848277165505491826404, +1.88749499723069393291317281282631323, +1.19509583604442017344377559754399511, +1.29117778274242514223057565511451993, +1.31363954850201147985985959414995358, +1.09138334308010992820639864734066801, +1.56154459751247302364856125715759584, +1.31704482170942646479013460676369927, +1.83440090213377346858545934365419845, +1.13370173433801683585813356231397636, +1.79861441368069235160907620231112666, +1.93212801270678228581846943674061845

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.69128244610153848277165505491826404, +1.88749499723069393291317281282631323, +1.19509583604442017344377559754399511, +1.29117778274242514223057565511451993, +1.31363954850201147985985959414995378, +1.09138334308010992820639864734066801, +1.56154459751247302364856125715759565, +1.31704482170942646479013460676369927, +1.83440090213377346858545934365419845, +1.13370173433801683585813356231397636, +1.79861441368069235160907620231112666, +1.93212801270678228581846943674061845, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33

96reltol = sqrt(epsilon(1._TKC))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, atad(1:size(data)), reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+40

106data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

107data

108(+1.07780612, +0.637313128), (+1.40441668, +0.555366397), (+1.47682309, +0.892937362), (+1.70211327, +0.299758911), (+1.97043943, +0.790941238), (+1.31449866, +0.522324979), (+1.87866187, +0.247500539E-1), (+1.03954840, +0.440327048), (+1.43759561, +0.422559559), (+1.48342419, +0.518446147), (+1.34857798, +0.362047672), (+1.79747415, +0.118052959), (+1.12648356, +0.134356618E-1), (+1.61003006, +0.472459078), (+1.21941423, +0.666978419), (+1.79749465, +0.917169988), (+1.03165901, +0.777861059), (+1.99063134, +0.914975762), (+1.66663373, +0.985779822), (+1.32103205, +0.967010260), (+1.61262786, +0.818169296), (+1.58384442, +0.164985776), (+1.45596790, +0.514289260), (+1.51967025, +0.490746140), (+1.70283234, +0.412917137), (+1.06995344, +0.497661948), (+1.14899540, +0.828314424E-1), (+1.97398615, +0.687692761), (+1.36629391, +0.423752010), (+1.19401658, +0.974453926), (+1.55580592, +0.389047861), (+1.86684012, +0.538112760), (+1.42667377, +0.923054338), (+1.39706981, +0.156732559), (+1.24116087, +0.137303948), (+1.63205361, +0.841006637), (+1.69712615, +0.764128327), (+1.64757049, +0.577376127), (+1.86639321, +0.976134896), (+1.67791939, +0.433986127)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.07780612, +0.637313128), (+1.40441656, +0.555366457), (+1.47682297, +0.892937183), (+1.70211303, +0.299758673), (+1.97043943, +0.790941060), (+1.31449854, +0.522324860), (+1.87866187, +0.247499645E-1), (+1.03954840, +0.440327048), (+1.43759561, +0.422559559), (+1.48342383, +0.518446207), (+1.34857798, +0.362047613), (+1.79747391, +0.118053034), (+1.12648344, +0.134357363E-1), (+1.61002970, +0.472459257), (+1.21941423, +0.666978359), (+1.79749465, +0.917169929), (+1.03165913, +0.777860999), (+1.99063122, +0.914975524), (+1.66663384, +0.985779583), (+1.32103217, +0.967009902), (+1.61262774, +0.818169236), (+1.58384442, +0.164985657), (+1.45596790, +0.514289141), (+1.51967025, +0.490746111), (+1.70283222, +0.412917078), (+1.06995320, +0.497661889), (+1.14899528, +0.828315020E-1), (+1.97398579, +0.687692523), (+1.36629355, +0.423752069), (+1.19401610, +0.974453807), (+1.55580568, +0.389047801), (+1.86683989, +0.538112521), (+1.42667377, +0.923054338), (+1.39706969, +0.156732559), (+1.24116075, +0.137303859), (+1.63205373, +0.841006517), (+1.69712615, +0.764128387), (+1.64757025, +0.577376187), (+1.86639333, +0.976134896), (+1.67791963, +0.433986068), (+0.596046448E-7, -0.447034836E-7), (+0.119209290E-6, -0.119209290E-6), (+0.298023224E-6, +0.149011612E-7), (+0.476837158E-6, +0.745058060E-7), (-0.119209290E-6, -0.149011612E-7), (+0.178813934E-6, -0.447034836E-7), (+0.596046448E-7, +0.119209290E-6), (+0.178813934E-6, -0.298023224E-7), (+0.00000000, +0.298023224E-7), (+0.119209290E-6, +0.149011612E-6), (+0.178813934E-6, +0.178813934E-6), (+0.119209290E-6, +0.268220901E-6), (+0.00000000, -0.178813934E-6), (+0.00000000, +0.00000000), (-0.596046448E-7, -0.119209290E-6), (+0.00000000, +0.149011612E-6), (+0.178813934E-6, -0.149011612E-7), (+0.596046448E-7, +0.596046448E-7), (+0.119209290E-6, +0.298023224E-7), (+0.357627869E-6, +0.208616257E-6), (+0.00000000, -0.163912773E-6), (+0.357627869E-6, +0.119209290E-6), (+0.596046448E-7, -0.447034836E-7), (+0.596046448E-7, +0.208616257E-6)

113reltol = sqrt(epsilon(1._TKC))

114reltol

115+0.345266977E-3

116isClose(data, atad(1:size(data)), reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+55

123data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

124data

125(+1.8204374295773031, +0.85648422583181238), (+1.4964091180601167, +0.28985631633129749), (+1.5159721443447536, +0.98020048190777109), (+1.6782832710547528, +0.15956651942530653), (+1.2037654255317314, +0.67117731732346697), (+1.0874862585679059, +0.93398645715623874), (+1.5021354253805783, +0.62474775746483024), (+1.7596208176073984, +0.21178746303560247), (+1.2152036952837024, +0.57013454906960659), (+1.0655183880565104, +0.58711880996285881E-1), (+1.2320637550039129, +0.59300166422872669), (+1.4947413458846746, +0.10091169537944433), (+1.3409531525609606, +0.77153351944788706), (+1.0163710397520094, +0.49906291797392366), (+1.7683205085532869, +0.66575697580339210E-1), (+1.5314262213851613, +0.44287343033713600), (+1.2054370529376528, +0.26481421076162859), (+1.8237584470881116, +0.72204360304441717), (+1.9203671564773002, +0.97196425866319713), (+1.6999071542103521, +0.97811434549690224), (+1.4382417956491986, +0.39720868862903158), (+1.1150578329863490, +0.96744877321278122), (+1.7823213370821249, +0.46986920312028890E-1), (+1.0443185975164115, +0.34138954467307070), (+1.1946718471697793, +0.57230836482490621), (+1.2050369286036391, +0.94271534974189397), (+1.3549419126731195, +0.48880896964910636), (+1.4779721278577891, +0.42079868970077206), (+1.0802791882169993, +0.60214534671940567), (+1.6073858713071356, +0.86083936314593279), (+1.0029406758715327, +0.54984766611809566), (+1.2772351072317345, +0.92859581838324901), (+1.6726704627893327, +0.51265530769321344), (+1.4611210763958740, +0.23241602103059644), (+1.1517594063507226, +0.55842559305294537), (+1.9952870633679658, +0.13766538470121414), (+1.3780462369066424, +0.62853018191329268), (+1.7453730497499989, +0.63845042168270771), (+1.5305113872723126, +0.68096477631164576), (+1.0723348671565589, +0.69014614830641974), (+1.1228829501121256, +0.20650442555681636), (+1.9473189061484300, +0.69242032620456995), (+1.1396743895034649, +0.99513435384533955), (+1.1766140945734858, +0.98479640323589024), (+1.1453315952961400, +0.55914309788329819), (+1.4787012443339456, +0.68328312332532037), (+1.5310303991254373, +0.93882384622710302), (+1.6400867034961715, +0.21381404405047455), (+1.2014167434486100, +0.85220583827887531), (+1.7711038032160218, +0.40045197876998917), (+1.1379469848560166, +0.35683802448215673E-1), (+1.7580938717794985, +0.47675258002980248), (+1.3814040375986292, +0.23839499982822465), (+1.1862828318197938, +0.50978199557752768), (+1.6036090233724121, +0.64840516605109322)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.8204374295773029, +0.85648422583181227), (+1.4964091180601169, +0.28985631633129727), (+1.5159721443447534, +0.98020048190777120), (+1.6782832710547528, +0.15956651942530689), (+1.2037654255317316, +0.67117731732346697), (+1.0874862585679057, +0.93398645715623863), (+1.5021354253805781, +0.62474775746483013), (+1.7596208176073982, +0.21178746303560270), (+1.2152036952837022, +0.57013454906960659), (+1.0655183880565107, +0.58711880996285826E-1), (+1.2320637550039126, +0.59300166422872691), (+1.4947413458846741, +0.10091169537944478), (+1.3409531525609608, +0.77153351944788717), (+1.0163710397520089, +0.49906291797392388), (+1.7683205085532860, +0.66575697580339710E-1), (+1.5314262213851608, +0.44287343033713650), (+1.2054370529376524, +0.26481421076162859), (+1.8237584470881116, +0.72204360304441717), (+1.9203671564773002, +0.97196425866319691), (+1.6999071542103521, +0.97811434549690202), (+1.4382417956491989, +0.39720868862903153), (+1.1150578329863488, +0.96744877321278089), (+1.7823213370821247, +0.46986920312028835E-1), (+1.0443185975164115, +0.34138954467307070), (+1.1946718471697793, +0.57230836482490610), (+1.2050369286036391, +0.94271534974189375), (+1.3549419126731195, +0.48880896964910614), (+1.4779721278577886, +0.42079868970077183), (+1.0802791882169998, +0.60214534671940556), (+1.6073858713071352, +0.86083936314593257), (+1.0029406758715329, +0.54984766611809544), (+1.2772351072317347, +0.92859581838324845), (+1.6726704627893325, +0.51265530769321332), (+1.4611210763958737, +0.23241602103059619), (+1.1517594063507224, +0.55842559305294515), (+1.9952870633679658, +0.13766538470121412), (+1.3780462369066424, +0.62853018191329268), (+1.7453730497499989, +0.63845042168270760), (+1.5305113872723124, +0.68096477631164554), (+1.0723348671565587, +0.69014614830641974), (+1.1228829501121254, +0.20650442555681608), (+1.9473189061484300, +0.69242032620457006), (+1.1396743895034647, +0.99513435384533910), (+1.1766140945734858, +0.98479640323588968), (+1.1453315952961403, +0.55914309788329808), (+1.4787012443339453, +0.68328312332532004), (+1.5310303991254368, +0.93882384622710258), (+1.6400867034961715, +0.21381404405047461), (+1.2014167434486098, +0.85220583827887519), (+1.7711038032160218, +0.40045197876998906), (+1.1379469848560166, +0.35683802448215840E-1), (+1.7580938717794985, +0.47675258002980214), (+1.3814040375986292, +0.23839499982822460), (+1.1862828318197935, +0.50978199557752746), (+1.6036090233724118, +0.64840516605109322), (+0.44408920985006262E-15, -0.83266726846886741E-16), (+0.0000000000000000, -0.55511151231257827E-16), (+0.0000000000000000, -0.11102230246251565E-15), (+0.55511151231257827E-15, +0.52735593669694936E-15), (+0.77715611723760958E-15, +0.44408920985006262E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.44408920985006262E-15, +0.55511151231257827E-15), (+0.33306690738754696E-15, +0.44408920985006262E-15)

130reltol = sqrt(epsilon(1._TKC))

131reltol

132+0.14901161193847656E-7

133isClose(data, atad(1:size(data)), reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+46

140data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

141data

142(+1.75382162782028155330725643323924021, +0.486344515785085935375825109486444456), (+1.28718957033698602013278864380797192, +0.392930636700125942553173372475894477), (+1.19786717712405182731078212270134473, +0.753527854429983351314184304538159479), (+1.32125106365828733186317436901683132, +0.910337605941109886012460879126090910), (+1.03225074895112255877184821920845005, +0.557468812312976776608387552375422920), (+1.42056915704951849333041691009733783, +0.920818243260667951551015790148705333), (+1.74161241011355682282681038021822643, +0.386076882160900372836951399202332537), (+1.22049339765795909834598206296483144, +0.138089418187268040994612504411936721E-1), (+1.23959782860177423103885412481115842, +0.522721551969889106771889736009015119), (+1.85693563828695655535367997708335771, +0.175386592717074778000323003049564847), (+1.61322291399865198737366145133878923, +0.657263389255564555452271117227032359), (+1.54237366080908449058772216713849443, +0.108708666526031852967518872770307174), (+1.53074578013171907185391098532218304, +0.803760490115993498624848189510966204), (+1.89172150857267875569372373380173206, +0.432504797068336317470818399476683635), (+1.71320962662164717850270423928740035, +0.846940659027582599904274806296599683), (+1.19132494985681207481670591669835856, +0.124172111865871016779990668317824576), (+1.89411641379863138450612035532989596, +0.488292358847107918091969048658748565), (+1.54408463934696268100565938300171146, +0.781712219795488164617478162330611354), (+1.58472175606030060859572413528153027, +0.677437108428520880353655476929984144), (+1.33776292004654103308208095466948710, +0.630779850533674972719731379153122753), (+1.23694648705235789942108747497413722, +0.850724556459336388737545247655353433), (+1.19714656683327860346210642224195811, +0.131552798267514125263835318492424597), (+1.75486111746712821048791073092278284, +0.525872832656699783310322783086854280), (+1.39950673405482664206395923894913849, +0.608939375091981430047199897366260591), (+1.01972454078232209520915943456754975, +0.853983919587548951579911249735044012), (+1.41333270554337454407213148542952770, +0.452405045160168491967738195622279920), (+1.24399402986477544395157631339080183, +0.733301326786570977909301321383296189), (+1.79830548003625820415387926799119185, +0.503130536815293691086470615480454586), (+1.90993838854329016966308487750740308, +0.540320368162744125224070859422991918), (+1.35319824098532178965892333713224280, +0.924226404879086716948198806834238638), (+1.99212705475873115973414115362043329, +0.585000818977075735228812880211522936), (+1.55653505628565469743797788676349431, +0.964544975286635872152653141977211894), (+1.38632421520098217805262359536547827, +0.695937781895883267635879211672728227), (+1.60896222591743045419484217373665141, +0.538824143315097636097681906081636518E-1), (+1.59176464063192328962974096744466745, +0.145906990707761017380389065316711879), (+1.20593672233664891427878555447663994, +0.624403883762612777914659429095012142), (+1.97793328102472424986065988782741458, +0.723868932204563765777045125389761906), (+1.38689978618016577339827638976289640, +0.765867354038757606156634061850139527), (+1.83939778876410970736333542622402416, +0.914122745022913763295222291108929555), (+1.30312099239804288104634096504156291, +0.470207658327252641535455117387005269), (+1.38443908354231527673997502741201330, +0.779186562443275773009906402637916244), (+1.95441713677190405528053600551109431, +0.808928414636610578665862728976283147), (+1.72800952964170679149131706953373547, +0.306168146291469041856132889453650062), (+1.16020560228011773665549222810197408, +0.985511117775031838989057782061826060), (+1.65136016290474787624363532222418926, +0.705799911230456327084167753266799776), (+1.15104654752985830360122399071978155, +0.752900071807158872366727095122001426)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.75382162782028155330725643323924021, +0.486344515785085935375825109486444408), (+1.28718957033698602013278864380797192, +0.392930636700125942553173372475894573), (+1.19786717712405182731078212270134435, +0.753527854429983351314184304538159672), (+1.32125106365828733186317436901683132, +0.910337605941109886012460879126090910), (+1.03225074895112255877184821920845005, +0.557468812312976776608387552375422535), (+1.42056915704951849333041691009733764, +0.920818243260667951551015790148705140), (+1.74161241011355682282681038021822662, +0.386076882160900372836951399202332441), (+1.22049339765795909834598206296483144, +0.138089418187268040994612504411935277E-1), (+1.23959782860177423103885412481115842, +0.522721551969889106771889736009015215), (+1.85693563828695655535367997708335732, +0.175386592717074778000323003049564895), (+1.61322291399865198737366145133878903, +0.657263389255564555452271117227032262), (+1.54237366080908449058772216713849404, +0.108708666526031852967518872770307415), (+1.53074578013171907185391098532218323, +0.803760490115993498624848189510966204), (+1.89172150857267875569372373380173226, +0.432504797068336317470818399476684020), (+1.71320962662164717850270423928740035, +0.846940659027582599904274806296599875), (+1.19132494985681207481670591669835856, +0.124172111865871016779990668317824769), (+1.89411641379863138450612035532989615, +0.488292358847107918091969048658748565), (+1.54408463934696268100565938300171185, +0.781712219795488164617478162330611354), (+1.58472175606030060859572413528153046, +0.677437108428520880353655476929984048), (+1.33776292004654103308208095466948710, +0.630779850533674972719731379153122561), (+1.23694648705235789942108747497413722, +0.850724556459336388737545247655353337), (+1.19714656683327860346210642224195811, +0.131552798267514125263835318492424549), (+1.75486111746712821048791073092278322, +0.525872832656699783310322783086854184), (+1.39950673405482664206395923894913888, +0.608939375091981430047199897366260591), (+1.01972454078232209520915943456754994, +0.853983919587548951579911249735044012), (+1.41333270554337454407213148542952808, +0.452405045160168491967738195622280017), (+1.24399402986477544395157631339080202, +0.733301326786570977909301321383296285), (+1.79830548003625820415387926799119185, +0.503130536815293691086470615480454393), (+1.90993838854329016966308487750740346, +0.540320368162744125224070859422992111), (+1.35319824098532178965892333713224280, +0.924226404879086716948198806834238638), (+1.99212705475873115973414115362043349, +0.585000818977075735228812880211522647), (+1.55653505628565469743797788676349431, +0.964544975286635872152653141977211797), (+1.38632421520098217805262359536547827, +0.695937781895883267635879211672728034), (+1.60896222591743045419484217373665141, +0.538824143315097636097681906081636759E-1), (+1.59176464063192328962974096744466764, +0.145906990707761017380389065316711783), (+1.20593672233664891427878555447664013, +0.624403883762612777914659429095012046), (+1.97793328102472424986065988782741458, +0.723868932204563765777045125389762194), (+1.38689978618016577339827638976289621, +0.765867354038757606156634061850139527), (+1.83939778876410970736333542622402435, +0.914122745022913763295222291108929748), (+1.30312099239804288104634096504156272, +0.470207658327252641535455117387005558), (+1.38443908354231527673997502741201330, +0.779186562443275773009906402637916147), (+1.95441713677190405528053600551109373, +0.808928414636610578665862728976283147), (+1.72800952964170679149131706953373566, +0.306168146291469041856132889453649821), (+1.16020560228011773665549222810197408, +0.985511117775031838989057782061825868), (+1.65136016290474787624363532222418868, +0.705799911230456327084167753266799969), (+1.15104654752985830360122399071978136, +0.752900071807158872366727095122001426), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-34), (+0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (+0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (+0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (+0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33), (+0.481482486096808963263994485646231830E-33, +0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33), (-0.674075480535532548569592279904724561E-33, +0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, +0.240741243048404481631997242823115915E-33)

147reltol = sqrt(epsilon(1._TKC))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, atad(1:size(data)), reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+18

157data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

158data

159+1.63905072, +1.24626052, +1.67990148, +1.04754066, +1.97469521, +1.17745018, +1.76495171, +1.24108291, +1.55421519, +1.81824172, +1.42525792, +1.18152046, +1.62974286, +1.29376769, +1.38798523, +1.28295279, +1.49665642, +1.78676748

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.63905072, +1.24626064, +1.67990148, +1.04754055, +1.97469497, +1.17745018, +1.76495147, +1.24108267, +1.55421543, +1.81824136, +1.42525816, +1.18152022, +1.62974310, +1.29376745, +1.38798535, +1.28295255, +1.49665642, +1.78676748, -0.119209290E-6, +0.00000000, +0.178813934E-6, +0.596046448E-7, +0.178813934E-6, +0.596046448E-7, -0.178813934E-6, +0.178813934E-6, -0.476837158E-6, +0.596046448E-7, -0.298023224E-6, +0.417232513E-6, -0.238418579E-6, +0.298023224E-6

164reltol = sqrt(epsilon(1._TKC))

165reltol

166+0.345266977E-3

167isClose(data, atad(1:size(data)), reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+19

174data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

175data

176+1.0326326255119498, +1.3140591376972621, +1.2014639362756419, +1.9650019412068986, +1.4241601486219384, +1.3804922425585984, +1.1323325489351999, +1.9408818304994564, +1.2670918802813040, +1.9769865138863980, +1.9325535638518945, +1.8951366849270288, +1.7134759541128846, +1.3899489597780121, +1.3880084903118697, +1.8269207419590356, +1.8441914381676949, +1.2951859841604958, +1.2110927710639632

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.0326326255119498, +1.3140591376972619, +1.2014639362756419, +1.9650019412068989, +1.4241601486219384, +1.3804922425585984, +1.1323325489351994, +1.9408818304994560, +1.2670918802813040, +1.9769865138863976, +1.9325535638518945, +1.8951366849270284, +1.7134759541128850, +1.3899489597780117, +1.3880084903118699, +1.8269207419590348, +1.8441914381676949, +1.2951859841604958, +1.2110927710639632, -0.22204460492503131E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.66613381477509392E-15

181reltol = sqrt(epsilon(1._TKC))

182reltol

183+0.14901161193847656E-7

184isClose(data, atad(1:size(data)), reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+57

191data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

192data

193+1.32315362879127289543946263253593895, +1.28205698410204782138846605099305971, +1.59750008463099713490787334552440634, +1.24286586468076415160269468642633115, +1.37979319021180173035816633818323948, +1.25487447115821696347104995479687929, +1.68119897605881597219485680469675562, +1.06233681024607328632630523620706314, +1.67447522546834237011903673446767463, +1.65305179288405658235645629614694680, +1.24157918812187618301286699811547661, +1.87389212605243187587508471194810516, +1.82485380057092147295079108809312599, +1.04547109225736359517352315060437703, +1.88952551791248598956894400547506068, +1.84455332980065337412657801044424837, +1.55093821983239498073774274163090918, +1.51115390805530520885838297481855237, +1.16168648919656116858345977316891647, +1.37425679222818690138734830540840801, +1.52667917962767370399738931141961446, +1.03367022612837474158653866662162697, +1.91305368967292111307620926352926177, +1.43041710292780513725370315540345183, +1.74731036902681561583577777769100133, +1.01375328464734673117508438431725150, +1.17081462235884542950040332507689387, +1.98103894853960723763204692876906610, +1.67119855141890542878134915519048120, +1.23221195553668673854079414647611168, +1.29251120929954726178043609185815648, +1.74732306580272580192998574740285345, +1.45667548969532468955968738269859464, +1.37188282855537260599808664074104819, +1.67082756065167459922838423627746015, +1.86813088949608370889578769716884765, +1.07034067169446125349357479383156526, +1.20880939932900576606880227490135385, +1.30081573028739903253940683795172244, +1.66182741091895484581603454302210813, +1.55542239997607701663016947673424879, +1.00813303055792412227052816892801506, +1.01426559287108035171357105739644529, +1.84853225526063825041211388569583304, +1.31919122552111930027877971442933163, +1.38548791804433688270160531766129776, +1.50411949802715972859335049132629214, +1.16498126738882574374309583935123226, +1.92568260782504865291994681978489943, +1.68402564370636100663901249471902246, +1.28475532001700203208360119986338238, +1.48534441429109748917193300817584777, +1.16745441040593710988176396005676449, +1.19342309625747889212192468445901236, +1.12833895406818276602959044443497489, +1.67244302566962807755370928275611146, +1.11584757357849444867487117097195998

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.32315362879127289543946263253593857, +1.28205698410204782138846605099305990, +1.59750008463099713490787334552440596, +1.24286586468076415160269468642633115, +1.37979319021180173035816633818323929, +1.25487447115821696347104995479687929, +1.68119897605881597219485680469675562, +1.06233681024607328632630523620706314, +1.67447522546834237011903673446767424, +1.65305179288405658235645629614694680, +1.24157918812187618301286699811547661, +1.87389212605243187587508471194810555, +1.82485380057092147295079108809312637, +1.04547109225736359517352315060437703, +1.88952551791248598956894400547506126, +1.84455332980065337412657801044424837, +1.55093821983239498073774274163090899, +1.51115390805530520885838297481855237, +1.16168648919656116858345977316891647, +1.37425679222818690138734830540840801, +1.52667917962767370399738931141961465, +1.03367022612837474158653866662162716, +1.91305368967292111307620926352926177, +1.43041710292780513725370315540345183, +1.74731036902681561583577777769100095, +1.01375328464734673117508438431725150, +1.17081462235884542950040332507689367, +1.98103894853960723763204692876906610, +1.67119855141890542878134915519048100, +1.23221195553668673854079414647611187, +1.29251120929954726178043609185815610, +1.74732306580272580192998574740285345, +1.45667548969532468955968738269859425, +1.37188282855537260599808664074104838, +1.67082756065167459922838423627746015, +1.86813088949608370889578769716884785, +1.07034067169446125349357479383156487, +1.20880939932900576606880227490135404, +1.30081573028739903253940683795172244, +1.66182741091895484581603454302210833, +1.55542239997607701663016947673424860, +1.00813303055792412227052816892801545, +1.01426559287108035171357105739644549, +1.84853225526063825041211388569583342, +1.31919122552111930027877971442933144, +1.38548791804433688270160531766129834, +1.50411949802715972859335049132629233, +1.16498126738882574374309583935123245, +1.92568260782504865291994681978489924, +1.68402564370636100663901249471902227, +1.28475532001700203208360119986338238, +1.48534441429109748917193300817584777, +1.16745441040593710988176396005676429, +1.19342309625747889212192468445901255, +1.12833895406818276602959044443497489, +1.67244302566962807755370928275611146, +1.11584757357849444867487117097195960, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33

198reltol = sqrt(epsilon(1._TKC))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, atad(1:size(data)), reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+84

208data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

209data

210(+1.15679598, +0.318929017), (+1.93784750, +0.689737380), (+1.67972016, +0.366448402), (+1.45633435, +0.605255365), (+1.00602102, +0.192348897), (+1.66079569, +0.522417128), (+1.77642488, +0.946146071), (+1.48306870, +0.904363751), (+1.41074789, +0.179871678), (+1.65211344, +0.279274642), (+1.08414209, +0.745483041E-1), (+1.56378913, +0.440233231), (+1.33866501, +0.604200721), (+1.48025441, +0.581844270), (+1.91753173, +0.228969932), (+1.02064228, +0.255574226), (+1.97409177, +0.620417714), (+1.58228803, +0.432087302), (+1.69038737, +0.662831247), (+1.83583164, +0.369925499E-1), (+1.85557222, +0.488001645), (+1.83251905, +0.755910277), (+1.73602235, +0.194308162), (+1.04883528, +0.123803556), (+1.77285242, +0.800968349), (+1.37650406, +0.205558777), (+1.97479749, +0.220135450E-1), (+1.48405957, +0.373969734), (+1.90391767, +0.145178199), (+1.88718510, +0.935977161), (+1.67585480, +0.398245573), (+1.53144455, +0.336304963), (+1.98121357, +0.291975796), (+1.00976491, +0.747411191), (+1.16318095, +0.461831987), (+1.13429856, +0.232117951), (+1.72760963, +0.531743944), (+1.97710443, +0.789391577), (+1.64613581, +0.140318453), (+1.11196029, +0.276460886), (+1.52131569, +0.384043038), (+1.58189547, +0.443499863), (+1.52180099, +0.858429909), (+1.72493923, +0.856699467), (+1.64929771, +0.174873173), (+1.82011676, +0.911653161), (+1.62609291, +0.644228458E-1), (+1.27205443, +0.952873349), (+1.99858248, +0.548946857), (+1.91550207, +0.686055064), (+1.36865711, +0.324822009), (+1.80546808, +0.281948209), (+1.05234599, +0.577670455), (+1.12472916, +0.503568053E-1), (+1.53141689, +0.491434157), (+1.43825722, +0.727533042), (+1.72009277, +0.112593710), (+1.31991863, +0.950670660), (+1.61594629, +0.479543686), (+1.75293088, +0.402393520), (+1.17840004, +0.428092420), (+1.92275703, +0.718535125), (+1.69787657, +0.692567110), (+1.84903193, +0.595223248), (+1.17603350, +0.454838276E-1), (+1.87879682, +0.188084185), (+1.05558574, +0.196561873), (+1.44901037, +0.111632347E-1), (+1.29661441, +0.591961145), (+1.32411194, +0.883917749), (+1.31820107, +0.151828587), (+1.19446111, +0.508436382), (+1.95784688, +0.116814315), (+1.40536284, +0.829741001), (+1.56042814, +0.322489560), (+1.38327956, +0.377744436E-1), (+1.48050869, +0.752282500), (+1.83148956, +0.692556620), (+1.30361009, +0.336199999E-1), (+1.97361982, +0.148808360E-1), (+1.70678377, +0.129279912), (+1.18353152, +0.844035327), (+1.92994928, +0.124877751), (+1.59252071, +0.205052793)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.15679598, +0.318928897), (+1.93784738, +0.689737558), (+1.67971969, +0.366448462), (+1.45633411, +0.605255365), (+1.00602078, +0.192348778), (+1.66079545, +0.522417068), (+1.77642477, +0.946145892), (+1.48306859, +0.904363513), (+1.41074800, +0.179871649), (+1.65211368, +0.279274821), (+1.08414221, +0.745483413E-1), (+1.56378925, +0.440233529), (+1.33866513, +0.604200602), (+1.48025441, +0.581844389), (+1.91753161, +0.228969961), (+1.02064204, +0.255574316), (+1.97409189, +0.620417833), (+1.58228803, +0.432087541), (+1.69038725, +0.662831306), (+1.83583128, +0.369927213E-1), (+1.85557222, +0.488001645), (+1.83251870, +0.755910218), (+1.73602223, +0.194308206), (+1.04883504, +0.123803675), (+1.77285266, +0.800968528), (+1.37650406, +0.205559179), (+1.97479749, +0.220137984E-1), (+1.48405933, +0.373969942), (+1.90391755, +0.145178303), (+1.88718486, +0.935977340), (+1.67585468, +0.398245692), (+1.53144431, +0.336305082), (+1.98121357, +0.291975617), (+1.00976491, +0.747411132), (+1.16318083, +0.461831808), (+1.13429868, +0.232117772), (+1.72760963, +0.531743646), (+1.97710419, +0.789391279), (+1.64613581, +0.140318260), (+1.11196017, +0.276460648), (+1.52131581, +0.384042978), (+1.58189559, +0.443499923), (+1.52180099, +0.858429790), (+1.72493887, +0.856699228), (+1.64929771, +0.174873054), (+1.82011652, +0.911653161), (+1.62609291, +0.644228235E-1), (+1.27205420, +0.952873111), (+1.99858248, +0.548946738), (+1.91550207, +0.686054945), (+1.36865711, +0.324821860), (+1.80546761, +0.281947941), (+1.05234599, +0.577670395), (+1.12472892, +0.503566861E-1), (+1.53141689, +0.491433918), (+1.43825686, +0.727532744), (+1.72009277, +0.112593710), (+1.31991827, +0.950670481), (+1.61594617, +0.479543507), (+1.75293052, +0.402393222), (+1.17839992, +0.428092301), (+1.92275667, +0.718534946), (+1.69787645, +0.692566991), (+1.84903193, +0.595222831), (+1.17603350, +0.454839021E-1), (+1.87879682, +0.188084126), (+1.05558586, +0.196561754), (+1.44901037, +0.111631453E-1), (+1.29661441, +0.591961145), (+1.32411170, +0.883917570), (+1.31820118, +0.151828647), (+1.19446123, +0.508436322), (+1.95784688, +0.116814457), (+1.40536261, +0.829741120), (+1.56042814, +0.322489589), (+1.38327944, +0.377744883E-1), (+1.48050869, +0.752282619), (+1.83148932, +0.692556679), (+1.30361021, +0.336202011E-1), (+1.97361970, +0.148809254E-1), (+1.70678389, +0.129279882), (+1.18353152, +0.844035268), (+1.92994928, +0.124877483), (+1.59252059, +0.205052525), (+0.178813934E-6, +0.223517418E-6), (+0.00000000, +0.596046448E-7), (+0.655651093E-6, +0.447034836E-7), (+0.476837158E-6, -0.596046448E-7), (-0.596046448E-7, -0.178813934E-6), (+0.00000000, -0.134110451E-6), (+0.298023224E-6, -0.163912773E-6), (-0.596046448E-7, -0.149011612E-6), (+0.178813934E-6, -0.745058060E-7), (-0.596046448E-7, -0.149011612E-6), (+0.178813934E-6, -0.193715096E-6), (+0.119209290E-6, -0.104308128E-6), (+0.596046448E-7, +0.163912773E-6), (-0.596046448E-7, +0.894069672E-7), (+0.00000000, +0.119209290E-6), (+0.119209290E-6, +0.283122063E-6), (-0.596046448E-7, +0.298023224E-6), (-0.119209290E-6, +0.298023224E-6), (+0.596046448E-7, +0.372529030E-6), (+0.178813934E-6, +0.283122063E-6), (+0.596046448E-7, -0.745058060E-7), (+0.00000000, -0.745058060E-7), (+0.00000000, +0.149011612E-6), (+0.596046448E-7, +0.268220901E-6), (+0.00000000, +0.00000000), (-0.596046448E-7, +0.298023224E-7), (-0.596046448E-7, +0.372529030E-7), (-0.178813934E-6, +0.119209290E-6), (+0.357627869E-6, +0.894069672E-7), (+0.178813934E-6, +0.298023224E-7), (+0.119209290E-6, +0.149011612E-6), (+0.298023224E-6, +0.268220901E-6), (+0.119209290E-6, +0.178813934E-6), (+0.119209290E-6, +0.208616257E-6), (+0.178813934E-6, +0.268220901E-6), (+0.119209290E-6, +0.119209290E-6), (+0.298023224E-6, -0.119209290E-6), (+0.238418579E-6, +0.00000000), (+0.238418579E-6, +0.745058060E-7), (+0.119209290E-6, +0.163912773E-6), (+0.119209290E-6, -0.894069672E-7), (+0.298023224E-6, +0.894069672E-7), (-0.596046448E-7, +0.298023224E-7), (-0.596046448E-7, +0.119209290E-6)

215reltol = sqrt(epsilon(1._TKC))

216reltol

217+0.345266977E-3

218isClose(data, atad(1:size(data)), reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+94

225data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

226data

227(+1.2011328650504494, +0.66060403454728045), (+1.8793112745053204, +0.50356503882704440), (+1.1501920445960701, +0.16234968779266712), (+1.9418156041720716, +0.42262844730627613), (+1.8983412586085793, +0.92717397621390296), (+1.4591353388612638, +0.89712698783891098E-1), (+1.3324334114366290, +0.64135491841027492), (+1.9192792031045789, +0.33926104500358678), (+1.7830757770297878, +0.65231533334393010), (+1.7012480248120276, +0.47938911728281719), (+1.5656640886494748, +0.99981841297980145), (+1.5510222052592018, +0.66973816787615881), (+1.2860184575177032, +0.95899864685109248), (+1.7757518266307799, +0.77808237116700252), (+1.4400625591364780, +0.28985630071244362), (+1.8521969124579656, +0.95583742850630593), (+1.5542545704220019, +0.87677193588675495), (+1.0205630098710008, +0.86904959062442944), (+1.8323231976855232, +0.96873624747264364), (+1.5494953284596120, +0.41787696934995155), (+1.6391499044129383, +0.78738869505042786), (+1.6357119484202065, +0.12177083373461495), (+1.5828346248744503, +0.89111488198357447), (+1.3412646194419433, +0.61515166173057978), (+1.0583729730274041, +0.86777092501312025), (+1.4848374563054398, +0.60522234778139983), (+1.6624461628112885, +0.75129307007234536), (+1.9457460694812001, +0.33638282622070892), (+1.1299180093142798, +0.91221229047097052), (+1.9775255903354052, +0.88730994471774161), (+1.0210988866191011, +0.95232059044376682), (+1.8116978803170158, +0.36293507303693306), (+1.4134232572598395, +0.89866945106165075), (+1.4523011031146886, +0.64768947366584817), (+1.7963684725227642, +0.50776256247086460), (+1.3043529550916508, +0.67090299226783501), (+1.6058854654524466, +0.70655712696286643), (+1.0881063474098740, +0.61074717457475602), (+1.7018553571485826, +0.28299761462867601), (+1.6728708051811239, +0.47039047744825513), (+1.0113524047383629, +0.84951460140489943), (+1.9713213345321923, +0.46133168261418567), (+1.6159011604942020, +0.18681819134787281E-1), (+1.4197705996965979, +0.75661846547345357), (+1.6541040273115875, +0.91565884934225861), (+1.8659549361120353, +0.52441682292934733), (+1.7667690006835790, +0.40452455200757009), (+1.8310372859490947, +0.69761883070080910), (+1.0378793337765302, +0.34737313330180908), (+1.8282680379752700, +0.95406396999469345), (+1.9934691144128052, +0.78780966299699917), (+1.6387471231400870, +0.38978219112837187), (+1.5651425096559981, +0.94146051112389262), (+1.8960565060237893, +0.53107328150581934), (+1.9086621493551410, +0.38484067855628035), (+1.2397955581020188, +0.93484440785961431), (+1.7949200713874061, +0.51035015313321574), (+1.7486888618301217, +0.74683766593616752E-1), (+1.5621336038214413, +0.25994494255829181), (+1.3678643184888291, +0.98480411865397965), (+1.1349479052368938, +0.15535361103801126), (+1.6887125702195931, +0.64205654005193102), (+1.1682630425427800, +0.51714790222575413E-1), (+1.6236367310734550, +0.78675251275627756), (+1.4158065333950018, +0.94533500048267061), (+1.1979177223650734, +0.96403535486865388), (+1.2379664566622166, +0.25703645254876673), (+1.4148201406458361, +0.73780990911046418), (+1.7033929066871631, +0.81726113756459240), (+1.6905817883795524, +0.46741300724413115), (+1.0109934955655344, +0.38094835608629440), (+1.6800551799264829, +0.53901849664382528), (+1.9201280711504185, +0.40276469844031226), (+1.3233595058052163, +0.68610290778842853), (+1.5508785547354336, +0.20527321963367851), (+1.4564421287714913, +0.50056204572649421), (+1.5669897517609646, +0.80176436260936201), (+1.6400969946840604, +0.81439805236273877), (+1.7407703887248431, +0.92788199924383719), (+1.1354582458285210, +0.39377156056029439), (+1.0060006529033534, +0.62721665507450031), (+1.6975897137124596, +0.15615348625997560), (+1.1270258533128019, +0.42776140084379521), (+1.0114867946412471, +0.18588284923376075), (+1.1029343750486502, +0.99025334892379413), (+1.8578650653416777, +0.40799903237534385), (+1.0076718331333354, +0.84055707060041307), (+1.3242004105121097, +0.83227800828701515), (+1.2052730590749361, +0.96711114549373978), (+1.5955003352126216, +0.25416206756307136), (+1.3714847660323868, +0.58524832056437937), (+1.2700728806407275, +0.25705644814765172), (+1.8965795736474096, +0.50808111291943869), (+1.0415089754177282, +0.53329334293513497)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.2011328650504494, +0.66060403454728034), (+1.8793112745053207, +0.50356503882704451), (+1.1501920445960696, +0.16234968779266723), (+1.9418156041720713, +0.42262844730627652), (+1.8983412586085793, +0.92717397621390285), (+1.4591353388612631, +0.89712698783891404E-1), (+1.3324334114366287, +0.64135491841027525), (+1.9192792031045787, +0.33926104500358728), (+1.7830757770297878, +0.65231533334393021), (+1.7012480248120274, +0.47938911728281752), (+1.5656640886494750, +0.99981841297980167), (+1.5510222052592013, +0.66973816787615925), (+1.2860184575177029, +0.95899864685109248), (+1.7757518266307795, +0.77808237116700296), (+1.4400625591364777, +0.28985630071244411), (+1.8521969124579649, +0.95583742850630649), (+1.5542545704220014, +0.87677193588675484), (+1.0205630098710006, +0.86904959062442955), (+1.8323231976855228, +0.96873624747264386), (+1.5494953284596114, +0.41787696934995189), (+1.6391499044129381, +0.78738869505042786), (+1.6357119484202063, +0.12177083373461525), (+1.5828346248744505, +0.89111488198357447), (+1.3412646194419429, +0.61515166173058022), (+1.0583729730274036, +0.86777092501312003), (+1.4848374563054396, +0.60522234778139994), (+1.6624461628112881, +0.75129307007234547), (+1.9457460694811997, +0.33638282622070942), (+1.1299180093142795, +0.91221229047097041), (+1.9775255903354045, +0.88730994471774149), (+1.0210988866191011, +0.95232059044376671), (+1.8116978803170152, +0.36293507303693318), (+1.4134232572598395, +0.89866945106165042), (+1.4523011031146886, +0.64768947366584806), (+1.7963684725227642, +0.50776256247086449), (+1.3043529550916506, +0.67090299226783512), (+1.6058854654524466, +0.70655712696286643), (+1.0881063474098740, +0.61074717457475625), (+1.7018553571485828, +0.28299761462867556), (+1.6728708051811236, +0.47039047744825502), (+1.0113524047383629, +0.84951460140489932), (+1.9713213345321920, +0.46133168261418578), (+1.6159011604942020, +0.18681819134787225E-1), (+1.4197705996965977, +0.75661846547345357), (+1.6541040273115875, +0.91565884934225839), (+1.8659549361120351, +0.52441682292934733), (+1.7667690006835788, +0.40452455200757009), (+1.8310372859490942, +0.69761883070080866), (+1.0378793337765297, +0.34737313330180897), (+1.8282680379752700, +0.95406396999469345), (+1.9934691144128052, +0.78780966299699906), (+1.6387471231400867, +0.38978219112837148), (+1.5651425096559985, +0.94146051112389229), (+1.8960565060237895, +0.53107328150581901), (+1.9086621493551412, +0.38484067855628001), (+1.2397955581020188, +0.93484440785961365), (+1.7949200713874056, +0.51035015313321530), (+1.7486888618301217, +0.74683766593616641E-1), (+1.5621336038214411, +0.25994494255829170), (+1.3678643184888291, +0.98480411865397943), (+1.1349479052368936, +0.15535361103801115), (+1.6887125702195929, +0.64205654005193069), (+1.1682630425427800, +0.51714790222575482E-1), (+1.6236367310734550, +0.78675251275627678), (+1.4158065333950018, +0.94533500048267083), (+1.1979177223650734, +0.96403535486865377), (+1.2379664566622166, +0.25703645254876689), (+1.4148201406458358, +0.73780990911046374), (+1.7033929066871631, +0.81726113756459218), (+1.6905817883795520, +0.46741300724413104), (+1.0109934955655344, +0.38094835608629418), (+1.6800551799264831, +0.53901849664382473), (+1.9201280711504185, +0.40276469844031232), (+1.3233595058052157, +0.68610290778842864), (+1.5508785547354338, +0.20527321963367895), (+1.4564421287714908, +0.50056204572649377), (+1.5669897517609643, +0.80176436260936201), (+1.6400969946840602, +0.81439805236273843), (+1.7407703887248429, +0.92788199924383696), (+1.1354582458285210, +0.39377156056029367), (+1.0060006529033529, +0.62721665507450008), (+1.6975897137124596, +0.15615348625997533), (+1.1270258533128019, +0.42776140084379521), (+1.0114867946412471, +0.18588284923376022), (+1.1029343750486502, +0.99025334892379391), (+1.8578650653416779, +0.40799903237534352), (+1.0076718331333354, +0.84055707060041318), (+1.3242004105121099, +0.83227800828701459), (+1.2052730590749354, +0.96711114549373955), (+1.5955003352126209, +0.25416206756307125), (+1.3714847660323866, +0.58524832056437925), (+1.2700728806407269, +0.25705644814765155), (+1.8965795736474091, +0.50808111291943847), (+1.0415089754177282, +0.53329334293513408), (+0.22204460492503131E-15, +0.0000000000000000), (+0.66613381477509392E-15, -0.38857805861880479E-15), (-0.44408920985006262E-15, -0.55511151231257827E-16), (-0.33306690738754696E-15, -0.55511151231257827E-16), (-0.55511151231257827E-15, +0.33306690738754696E-15), (-0.22204460492503131E-15, -0.11102230246251565E-15), (-0.11102230246251565E-15, +0.33306690738754696E-15), (-0.22204460492503131E-15, -0.22204460492503131E-15), (+0.0000000000000000, +0.30531133177191805E-15), (+0.33306690738754696E-15, +0.0000000000000000), (-0.33306690738754696E-15, -0.55511151231257827E-16), (-0.22204460492503131E-15, -0.22204460492503131E-15), (+0.0000000000000000, -0.55511151231257827E-16), (-0.22204460492503131E-15, -0.16653345369377348E-15), (-0.33306690738754696E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, -0.27755575615628914E-15), (-0.22204460492503131E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.13877787807814457E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.38857805861880479E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.72164496600635175E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (-0.11102230246251565E-15, +0.69388939039072284E-15), (+0.55511151231257827E-15, +0.49960036108132044E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, -0.55511151231257827E-16), (-0.11102230246251565E-15, +0.24980018054066022E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.61062266354383610E-15), (+0.22204460492503131E-15, +0.70776717819853729E-15), (+0.44408920985006262E-15, +0.99920072216264089E-15)

232reltol = sqrt(epsilon(1._TKC))

233reltol

234+0.14901161193847656E-7

235isClose(data, atad(1:size(data)), reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+32

242data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

243data

244(+1.68151671027262356108358250245209111, +0.776193799570554650425607589084578768), (+1.59749058547821634412555554027198008, +0.953419763789632533047114944672809064), (+1.30492358145473645308148907017491184, +0.606300198951384936236158527678387506), (+1.25791520220200254387475917370102252, +0.910613165434533164275398253683234335), (+1.05256215689102474858371567637081019, +0.379743568334660852528112762000406580), (+1.34481423734875607567681317459675405, +0.411957354424187918282367332377750363E-1), (+1.45417119395327934384111815204918228, +0.232389883994453840161752527773493793), (+1.52916048469093898363794209725644363, +0.340001644775345157019389131675880852), (+1.09282286156846524600233250520653727, +0.918760334048631936171164068107654409), (+1.73140593353104130932934437825254993, +0.723436475378616253837742589623028821), (+1.09160144443666284434829388215482354, +0.623541937050628761367170303883732516), (+1.30670629216600376276797205244157238, +0.925610575008859225787848227307768572), (+1.43054480764682825283859954272212528, +0.317626406739413282866492184017871795), (+1.38905561464776073885708530802168599, +0.925846562895429153477061931640124478), (+1.57732010420671977452536202515911113, +0.896542855865022388415655814230253537), (+1.85888402668706661451245028679452808, +0.202646598551819261888688887345152383), (+1.67740033490494337887600467720595820, +0.798580795686819130769360326555610176), (+1.42415812970227201969185063038054046, +0.567577911738966574697403704396529394), (+1.45915979775695712687191061160713792, +0.861946537914974966668326276685117736), (+1.83537787943017541312495404598905866, +0.769656998404604203696177714109777913), (+1.95871816579732917074887593313270595, +0.162428497650495177555522281112432401), (+1.59420672214825432879089044935634235, +0.606501050046762666020448525675415068), (+1.86762616676340428009224741255086553, +0.126403343748729882478860086281636544E-1), (+1.58575791062574875236204281936821041, +0.332882944709475879406147183235525172), (+1.33688185954777170041029579391364762, +0.274500192867960407541719501291428083), (+1.58728598479720328608945906723985209, +0.774506918762560049358348496074631476), (+1.30563998642670822858267474558974062, +0.422619766686505146517773930286739321), (+1.07596637053412837328888442113032179, +0.235897522939261172975277567725971332E-1), (+1.44098317328665090568925748763704910, +0.436952022700539523723719773459910283), (+1.17483757177713449056384928667554782, +0.406448365468087726903469747126205708), (+1.30226923509744857631161975868235474, +0.648177114008934716510592223724297601), (+1.27571247645428351311689638077746669, +0.183353687052432723858970256094731675)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.68151671027262356108358250245209130, +0.776193799570554650425607589084578672), (+1.59749058547821634412555554027198027, +0.953419763789632533047114944672808967), (+1.30492358145473645308148907017491184, +0.606300198951384936236158527678387313), (+1.25791520220200254387475917370102233, +0.910613165434533164275398253683234528), (+1.05256215689102474858371567637080980, +0.379743568334660852528112762000406580), (+1.34481423734875607567681317459675425, +0.411957354424187918282367332377750363E-1), (+1.45417119395327934384111815204918247, +0.232389883994453840161752527773493504), (+1.52916048469093898363794209725644363, +0.340001644775345157019389131675880852), (+1.09282286156846524600233250520653746, +0.918760334048631936171164068107654313), (+1.73140593353104130932934437825254993, +0.723436475378616253837742589623028821), (+1.09160144443666284434829388215482374, +0.623541937050628761367170303883732419), (+1.30670629216600376276797205244157219, +0.925610575008859225787848227307768572), (+1.43054480764682825283859954272212528, +0.317626406739413282866492184017871651), (+1.38905561464776073885708530802168637, +0.925846562895429153477061931640124478), (+1.57732010420671977452536202515911113, +0.896542855865022388415655814230253537), (+1.85888402668706661451245028679452808, +0.202646598551819261888688887345152407), (+1.67740033490494337887600467720595839, +0.798580795686819130769360326555610080), (+1.42415812970227201969185063038054046, +0.567577911738966574697403704396529394), (+1.45915979775695712687191061160713792, +0.861946537914974966668326276685117543), (+1.83537787943017541312495404598905846, +0.769656998404604203696177714109778202), (+1.95871816579732917074887593313270575, +0.162428497650495177555522281112432329), (+1.59420672214825432879089044935634274, +0.606501050046762666020448525675415165), (+1.86762616676340428009224741255086572, +0.126403343748729882478860086281633775E-1), (+1.58575791062574875236204281936821041, +0.332882944709475879406147183235525364), (+1.33688185954777170041029579391364781, +0.274500192867960407541719501291428034), (+1.58728598479720328608945906723985209, +0.774506918762560049358348496074631476), (+1.30563998642670822858267474558974081, +0.422619766686505146517773930286739321), (+1.07596637053412837328888442113032159, +0.235897522939261172975277567725972295E-1), (+1.44098317328665090568925748763704910, +0.436952022700539523723719773459910331), (+1.17483757177713449056384928667554801, +0.406448365468087726903469747126205948), (+1.30226923509744857631161975868235474, +0.648177114008934716510592223724297505), (+1.27571247645428351311689638077746688, +0.183353687052432723858970256094731796)

249reltol = sqrt(epsilon(1._TKC))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, atad(1:size(data)), reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+53

259data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

260data

261+1.62005734, +1.61296964, +1.42182636, +1.36385036, +1.89776146, +1.90176725, +1.43759727, +1.99714899, +1.70265782, +1.60153496, +1.84932768, +1.12582469, +1.74980998, +1.60258842, +1.30701923, +1.94706130, +1.88078284, +1.61026168, +1.84173179, +1.48613238, +1.29887652, +1.17759109, +1.46872032, +1.89137554, +1.01684058, +1.12013328, +1.50230169, +1.28955758, +1.77340817, +1.92151999, +1.19861603, +1.25574255, +1.31792688, +1.08787191, +1.03690839, +1.97255015, +1.83843243, +1.40834689, +1.01001883, +1.70343804, +1.83889866, +1.35955048, +1.60809326, +1.79602027, +1.15513945, +1.26849771, +1.92047346, +1.81460702, +1.54595602, +1.37139142, +1.33700657, +1.28818941, +1.58734918

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.62005734, +1.61296952, +1.42182612, +1.36385036, +1.89776134, +1.90176725, +1.43759716, +1.99714899, +1.70265770, +1.60153496, +1.84932733, +1.12582469, +1.74980998, +1.60258853, +1.30701935, +1.94706118, +1.88078260, +1.61026180, +1.84173167, +1.48613250, +1.29887629, +1.17759120, +1.46872032, +1.89137578, +1.01684046, +1.12013364, +1.50230145, +1.28955781, +1.77340794, +1.92152023, +1.19861603, +1.25574255, +1.31792688, +1.08787191, +1.03690839, +1.97255015, +1.83843231, +1.40834665, +1.01001894, +1.70343828, +1.83889866, +1.35955036, +1.60809302, +1.79602003, +1.15513945, +1.26849759, +1.92047346, +1.81460702, +1.54595590, +1.37139142, +1.33700645, +1.28818953, +1.58734894, +0.119209290E-6, +0.119209290E-6, +0.298023224E-6, +0.596046448E-7, +0.298023224E-6, +0.596046448E-7, +0.357627869E-6, +0.178813934E-6, +0.119209290E-6, +0.596046448E-7, +0.596046448E-7

266reltol = sqrt(epsilon(1._TKC))

267reltol

268+0.345266977E-3

269isClose(data, atad(1:size(data)), reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+48

276data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

277data

278+1.9119314008078154, +1.7894658439524762, +1.5173036703678522, +1.4366814100527823, +1.2883557488412405, +1.2639098394112520, +1.2714621726539144, +1.5040969857121500, +1.7768448911918213, +1.0450257821828286, +1.4498883520268788, +1.5922306171062772, +1.4579149834967611, +1.7113634136178000, +1.5322833868265531, +1.8860876738779315, +1.3394889540707930, +1.8175326501509321, +1.8474540330522675, +1.8410530500041717, +1.4413662620609422, +1.2683417224148805, +1.6650344520165929, +1.2616505340766686, +1.7942294386161417, +1.6353221594298173, +1.7226251069325880, +1.7781238540338777, +1.3564589738185688, +1.0892482675943831, +1.0625614771719714, +1.7283831977973270, +1.2236412862962711, +1.6657209131850035, +1.6291603197178324, +1.1416000129849004, +1.5928975833656898, +1.8280030157021729, +1.9583168435880804, +1.0470490746043271, +1.4471344353577589, +1.1883289813296458, +1.5947100341131475, +1.0561713644723754, +1.7061729137544854, +1.8467174389899514, +1.1159953695090428, +1.9987815136324669

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.9119314008078157, +1.7894658439524762, +1.5173036703678517, +1.4366814100527823, +1.2883557488412412, +1.2639098394112522, +1.2714621726539144, +1.5040969857121500, +1.7768448911918213, +1.0450257821828286, +1.4498883520268788, +1.5922306171062766, +1.4579149834967613, +1.7113634136178000, +1.5322833868265526, +1.8860876738779313, +1.3394889540707933, +1.8175326501509321, +1.8474540330522675, +1.8410530500041711, +1.4413662620609422, +1.2683417224148801, +1.6650344520165925, +1.2616505340766682, +1.7942294386161421, +1.6353221594298168, +1.7226251069325877, +1.7781238540338764, +1.3564589738185688, +1.0892482675943829, +1.0625614771719714, +1.7283831977973263, +1.2236412862962716, +1.6657209131850035, +1.6291603197178326, +1.1416000129849000, +1.5928975833656902, +1.8280030157021729, +1.9583168435880802, +1.0470490746043268, +1.4471344353577598, +1.1883289813296454, +1.5947100341131475, +1.0561713644723745, +1.7061729137544857, +1.8467174389899514, +1.1159953695090428, +1.9987815136324663, +0.33306690738754696E-15, -0.44408920985006262E-15, +0.77715611723760958E-15, -0.33306690738754696E-15, +0.77715611723760958E-15, -0.44408920985006262E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.66613381477509392E-15

283reltol = sqrt(epsilon(1._TKC))

284reltol

285+0.14901161193847656E-7

286isClose(data, atad(1:size(data)), reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+30

293data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

294data

295+1.18356110870828642819875850416782713, +1.48085570675410656339949748647264800, +1.65047785523402339242073895260849791, +1.29942348411088858913225789885809141, +1.57755581517641753870920637036914218, +1.76188163199849025164642368443135768, +1.15516896847323125344744530272447763, +1.12834461777421630555527800228289228, +1.69728756529823186177157242776730795, +1.33630798282102921158794055275215729, +1.34039860941634602388394204077305226, +1.78259242688978576925255888387455252, +1.38542003803789502543005360859066461, +1.42782645518204384875885698396549260, +1.84082534175032454687512419650752076, +1.73728315579190615431473029807547619, +1.23908893370809572402465952338875673, +1.97210935021209507784539351100832064, +1.01345336907327333096864455676212229, +1.53061707179606132995259069351317777, +1.54522242052632132327387769478919455, +1.62380361405096255209587534372787289, +1.54132295374758753508541470095393434, +1.58306896577960775178010119412494424, +1.13188405786205635028005718815717070, +1.78160694595849775660072671848807782, +1.81719907272008690261738958342156756, +1.57506043780306332876553133571915627, +1.69744215378107988260663337011406855, +1.27817215126690958744821355427311848

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.18356110870828642819875850416782694, +1.48085570675410656339949748647264800, +1.65047785523402339242073895260849791, +1.29942348411088858913225789885809121, +1.57755581517641753870920637036914199, +1.76188163199849025164642368443135749, +1.15516896847323125344744530272447743, +1.12834461777421630555527800228289209, +1.69728756529823186177157242776730795, +1.33630798282102921158794055275215729, +1.34039860941634602388394204077305226, +1.78259242688978576925255888387455271, +1.38542003803789502543005360859066442, +1.42782645518204384875885698396549241, +1.84082534175032454687512419650752076, +1.73728315579190615431473029807547619, +1.23908893370809572402465952338875654, +1.97210935021209507784539351100832044, +1.01345336907327333096864455676212191, +1.53061707179606132995259069351317757, +1.54522242052632132327387769478919435, +1.62380361405096255209587534372787270, +1.54132295374758753508541470095393434, +1.58306896577960775178010119412494424, +1.13188405786205635028005718815717051, +1.78160694595849775660072671848807801, +1.81719907272008690261738958342156756, +1.57506043780306332876553133571915627, +1.69744215378107988260663337011406874, +1.27817215126690958744821355427311810, -0.481482486096808963263994485646231830E-33, -0.288889491658085377958396691387739098E-33

300reltol = sqrt(epsilon(1._TKC))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, atad(1:size(data)), reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+83

310data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

311data

312(+1.64248192, +0.820950091), (+1.30868816, +0.772174954), (+1.93659425, +0.455860198), (+1.30357432, +0.736014247E-1), (+1.21131229, +0.275605917E-1), (+1.44088757, +0.924879730), (+1.59385026, +0.156688690), (+1.10294843, +0.951149583), (+1.43805993, +0.418365359), (+1.42672539, +0.820008755), (+1.68262672, +0.403605163), (+1.42055559, +0.795987368), (+1.15380263, +0.128438711), (+1.78318143, +0.296790600E-1), (+1.65099430, +0.873233736), (+1.42825294, +0.179407895), (+1.98695016, +0.316660762), (+1.79327857, +0.360620439), (+1.70541477, +0.194416165), (+1.15451956, +0.733778000), (+1.03191590, +0.565721989), (+1.41781592, +0.578004658), (+1.20119166, +0.758268476), (+1.69037104, +0.646849096), (+1.96640587, +0.645386159), (+1.73633158, +0.350212634), (+1.04336286, +0.334354639E-1), (+1.36737943, +0.957827985), (+1.40216541, +0.869738340), (+1.68087113, +0.786046326), (+1.98729920, +0.186604917), (+1.07321072, +0.855953336), (+1.45623231, +0.742604494), (+1.77807117, +0.427476764E-1), (+1.19053936, +0.711212575), (+1.46190083, +0.940478265), (+1.42750144, +0.444103539), (+1.12659144, +0.925655425), (+1.43795466, +0.363725543), (+1.24223542, +0.557476819), (+1.91575170, +0.565181673), (+1.86359572, +0.692117691), (+1.23011088, +0.748953819E-1), (+1.92716730, +0.586193442), (+1.70532441, +0.119671643), (+1.00889122, +0.618925631), (+1.14071321, +0.191957951), (+1.63841903, +0.665013194E-1), (+1.66653085, +0.870574057), (+1.07696486, +0.911551654), (+1.55750084, +0.482573092), (+1.41708684, +0.510431588), (+1.38573217, +0.710082054E-1), (+1.90928924, +0.270240247), (+1.33109856, +0.668291628), (+1.37456226, +0.485804081), (+1.78692806, +0.254137337), (+1.67347884, +0.682129741), (+1.27999902, +0.212170959), (+1.01006174, +0.680307508), (+1.34038639, +0.314635575), (+1.79271531, +0.769351602), (+1.66197228, +0.281244099), (+1.72761393, +0.897957146), (+1.29016840, +0.218777537), (+1.62691259, +0.263310730), (+1.31908655, +0.336975932), (+1.68801379, +0.525721550), (+1.78024626, +0.113105416), (+1.64256120, +0.409950078), (+1.74754322, +0.934445858E-2), (+1.29964685, +0.429670811), (+1.37783480, +0.593276918), (+1.92762160, +0.378936112), (+1.62385643, +0.999376476), (+1.46238685, +0.542595088), (+1.13493109, +0.774851322), (+1.81851590, +0.783778012), (+1.43441606, +0.624859512), (+1.13640785, +0.103294134), (+1.20774317, +0.339832902), (+1.89233267, +0.934469879), (+1.90571928, +0.646388710)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.64248204, +0.820950150), (+1.30868793, +0.772174954), (+1.93659401, +0.455860198), (+1.30357397, +0.736014396E-1), (+1.21131229, +0.275605470E-1), (+1.44088745, +0.924879670), (+1.59385014, +0.156688526), (+1.10294843, +0.951149464), (+1.43805993, +0.418365508), (+1.42672563, +0.820008755), (+1.68262684, +0.403605312), (+1.42055559, +0.795987368), (+1.15380287, +0.128438771), (+1.78318167, +0.296792090E-1), (+1.65099430, +0.873233736), (+1.42825305, +0.179407895), (+1.98695040, +0.316660881), (+1.79327869, +0.360620499), (+1.70541465, +0.194416314), (+1.15451956, +0.733778000), (+1.03191578, +0.565721929), (+1.41781592, +0.578004539), (+1.20119166, +0.758268476), (+1.69037104, +0.646848977), (+1.96640575, +0.645386219), (+1.73633170, +0.350212902), (+1.04336286, +0.334355682E-1), (+1.36737919, +0.957827926), (+1.40216541, +0.869738340), (+1.68087101, +0.786046505), (+1.98729897, +0.186605051), (+1.07321095, +0.855953336), (+1.45623255, +0.742604434), (+1.77807093, +0.427476019E-1), (+1.19053936, +0.711212158), (+1.46190071, +0.940478206), (+1.42750120, +0.444103301), (+1.12659144, +0.925655246), (+1.43795478, +0.363725364), (+1.24223554, +0.557476759), (+1.91575170, +0.565181613), (+1.86359560, +0.692117631), (+1.23011088, +0.748951733E-1), (+1.92716718, +0.586193383), (+1.70532453, +0.119671524), (+1.00889111, +0.618925512), (+1.14071321, +0.191957787), (+1.63841927, +0.665013492E-1), (+1.66653097, +0.870573878), (+1.07696462, +0.911551595), (+1.55750072, +0.482572794), (+1.41708684, +0.510431468), (+1.38573217, +0.710080266E-1), (+1.90928888, +0.270240068), (+1.33109856, +0.668291450), (+1.37456238, +0.485803723), (+1.78692782, +0.254137337), (+1.67347860, +0.682129860), (+1.27999902, +0.212170929), (+1.01006162, +0.680307269), (+1.34038627, +0.314635456), (+1.79271519, +0.769351482), (+1.66197205, +0.281243980), (+1.72761369, +0.897957087), (+1.29016852, +0.218777537), (+1.62691236, +0.263310879), (+1.31908655, +0.336975753), (+1.68801367, +0.525721371), (+1.78024626, +0.113105237), (+1.64256120, +0.409950107), (+1.74754333, +0.934420526E-2), (+1.29964709, +0.429670841), (+1.37783468, +0.593276858), (+1.92762136, +0.378936261), (+1.62385643, +0.999376416), (+1.46238661, +0.542595148), (+1.13493109, +0.774851322), (+1.81851578, +0.783778191), (+1.43441629, +0.624859631), (+1.13640797, +0.103294194), (+1.20774317, +0.339832962), (+1.89233232, +0.934469938), (+1.90571916, +0.646388412), (+0.178813934E-6, -0.208616257E-6), (+0.238418579E-6, +0.119209290E-6), (+0.178813934E-6, +0.178813934E-6), (+0.417232513E-6, +0.208616257E-6), (+0.357627869E-6, +0.119209290E-6), (+0.119209290E-6, -0.149011612E-6), (-0.596046448E-7, -0.149011612E-6), (+0.178813934E-6, -0.447034836E-7), (-0.596046448E-7, -0.149011612E-6), (-0.119209290E-6, -0.208616257E-6), (+0.596046448E-7, -0.119209290E-6), (+0.119209290E-6, -0.104308128E-6), (+0.00000000, +0.298023224E-7), (+0.596046448E-7, +0.596046448E-7), (-0.596046448E-7, +0.223517418E-6), (+0.596046448E-7, +0.208616257E-6), (+0.00000000, +0.149011612E-6), (+0.596046448E-7, +0.178813934E-6), (-0.596046448E-7, +0.327825546E-6), (+0.119209290E-6, +0.357627869E-6), (-0.119209290E-6, +0.268220901E-6), (+0.178813934E-6, +0.298023224E-7), (+0.119209290E-6, +0.00000000), (+0.178813934E-6, -0.298023224E-7), (+0.596046448E-7, +0.178813934E-6), (+0.119209290E-6, +0.00000000), (-0.596046448E-7, -0.596046448E-7), (+0.178813934E-6, +0.223517418E-6), (+0.00000000, +0.149011612E-6), (+0.238418579E-6, +0.149011612E-6), (-0.596046448E-7, +0.894069672E-7), (+0.357627869E-6, +0.134110451E-6), (+0.178813934E-6, +0.298023224E-6), (+0.178813934E-6, +0.238418579E-6), (+0.596046448E-7, +0.312924385E-6), (+0.357627869E-6, +0.327825546E-6), (+0.238418579E-6, +0.417232513E-6), (+0.357627869E-6, +0.149011612E-7), (+0.298023224E-6, -0.149011612E-6), (+0.298023224E-6, +0.372529030E-7), (+0.119209290E-6, +0.119209290E-6), (+0.238418579E-6, +0.00000000), (+0.238418579E-6, +0.894069672E-7), (+0.119209290E-6, +0.163912773E-6), (+0.178813934E-6, +0.596046448E-7)

317reltol = sqrt(epsilon(1._TKC))

318reltol

319+0.345266977E-3

320isClose(data, atad(1:size(data)), reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+8

327data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

328data

329(+1.3058520436045646, +0.19229431255520002), (+1.0771773541486573, +0.55839503549732961), (+1.0438819801864105, +0.87106907326759597), (+1.5658869226465608, +0.44915142633881944), (+1.4430039494037157, +0.86307128244171538), (+1.5438457301976749, +0.62080808652293296), (+1.0480835941451234, +0.53859702165498879), (+1.0783135525701621, +0.99122374905253163)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.3058520436045646, +0.19229431255520002), (+1.0771773541486578, +0.55839503549732949), (+1.0438819801864105, +0.87106907326759586), (+1.5658869226465608, +0.44915142633881955), (+1.4430039494037157, +0.86307128244171538), (+1.5438457301976749, +0.62080808652293284), (+1.0480835941451234, +0.53859702165498868), (+1.0783135525701626, +0.99122374905253141)

334reltol = sqrt(epsilon(1._TKC))

335reltol

336+0.14901161193847656E-7

337isClose(data, atad(1:size(data)), reltol = reltol)

338T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+69

344data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

345data

346(+1.89136171043111535634097477129178789, +0.264848477575108764133306718472938375), (+1.99158268325345291907706014084017652, +0.675705547911220038517775498145750098), (+1.66468088345354178773515292743919791, +0.171141618194105855427721165335930146), (+1.22843285201271987289845199045782874, +0.321034611010014852613403501121998928), (+1.10300633858458604730062274130549508, +0.847997830687805709234282673189815045), (+1.56098437247272100679491694176848298, +0.982199234840859056042877930112474952), (+1.59213081181107014223653684178902858, +0.974512734841776565231767683360052061E-1), (+1.20959405260618643850984506188244623, +0.143415527333347578567544489995199791), (+1.08625922556930308569118818196430354, +0.194470497463577091655713540202078715), (+1.21920424640543212573040237059507162, +0.678329397815035943606568254355286336), (+1.45512998958644034743734013382646089, +0.568193384077471258863786019258328046), (+1.55453432381310942729070113894831805, +0.781180044392367043062621072308467318), (+1.18061099284831948472659647248934388, +0.716053925173319038367007077802319593), (+1.99268859030608600243473615890090031, +0.169154289644104534366474280993714944), (+1.33724549273132567627427796051116213, +0.187958393685235873903444489697541265), (+1.67295199979029591518690698848236723, +0.772431715310192695055419699165602407), (+1.45175797823986950670546111661689536, +0.485727697376615532536179705473211888), (+1.31621132095950067102368697579147283, +0.160640366691489102063588419398819253), (+1.36369670554037641065739227309183814, +0.197114169150090632720592837203854644), (+1.14779325933790249717848003298735195, +0.873275651424366729755860023610778345), (+1.25293156493832904305482437567987499, +0.536832821056239470534287338972706424), (+1.89731339512536852857263433259492945, +0.650551373026976659362725133630643954), (+1.72317390247008545354740675074130001, +0.769396488829382409891750750028904693), (+1.09355681204571955534852476033460626, +0.658146736902353985209049120659410994), (+1.85920894020673889488340264908076188, +0.212473734916154474817887434401635062), (+1.27941482396874231786402854578860839, +0.638810435326171240353504683585068688), (+1.85279822459997621215260368264407194, +0.590723087444267670539374506786459834), (+1.92756424602919567587179899928362312, +0.956601955798877002859335781128626188), (+1.17279735457989031713927352200150985, +0.587874235287059160445180865827368991), (+1.24549701936917023427848384452016333, +0.662762980021179157044931059426922440), (+1.48217654198757785232488704687650138, +0.770889648115416675145130058553293813E-1), (+1.82423788208635820790966896745112326, +0.434444446237282986868357962690085369), (+1.07856934887290680317242390392022218, +0.279900791561162875066253917278570775), (+1.78721247792703164214629726807589491, +0.688494214076323156565449734593604973), (+1.85354699231318376418905564848438613, +0.304270555787297583976989388148823685), (+1.31590196603734831563925519808796343, +0.282824718547156696981790073776800230), (+1.00785792821472711062665562093643075, +0.559905429745324495521542891920486010), (+1.32197746028449188805104796305002141, +0.225631119160857967146407891548418478), (+1.82217665090249552401374667390481714, +0.948125015132555840040343833881874063), (+1.54440111551059599678589129833565315, +0.406834034402513814881923533642350521E-1), (+1.98707303987231785755465130996376977, +0.676522364509264001939596147213489231), (+1.43881702201412012997820020851051439, +0.674911769274646979952262160957387036), (+1.12586878359442080916234227990842448, +0.609597551944003642422715415387711970), (+1.13601557294685817374041954858485232, +0.420409013857039463713380353514861054), (+1.94537863822338980871874313633035664, +0.254968927881533129211660878167394583), (+1.61443479196128539573407220471446831, +0.540419769336310776049665539996192241), (+1.74296629609587600450038301142093996, +0.975135599678014277888591392388678158), (+1.12603680844138996430123372280243606, 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347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.89136171043111535634097477129178789, +0.264848477575108764133306718472938567), (+1.99158268325345291907706014084017672, +0.675705547911220038517775498145749809), (+1.66468088345354178773515292743919791, +0.171141618194105855427721165335930002), (+1.22843285201271987289845199045782893, +0.321034611010014852613403501121998736), (+1.10300633858458604730062274130549469, +0.847997830687805709234282673189815045), (+1.56098437247272100679491694176848298, +0.982199234840859056042877930112474470), (+1.59213081181107014223653684178902858, +0.974512734841776565231767683360051580E-1), (+1.20959405260618643850984506188244623, +0.143415527333347578567544489995199261), (+1.08625922556930308569118818196430354, +0.194470497463577091655713540202078787), (+1.21920424640543212573040237059507181, +0.678329397815035943606568254355286240), (+1.45512998958644034743734013382646127, +0.568193384077471258863786019258328335), (+1.55453432381310942729070113894831843, 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(-0.385185988877447170611195588516985464E-33, +0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, -0.120370621524202240815998621411557957E-33), (-0.577778983316170755916793382775478196E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.325000678115346050203196277811206485E-33), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), 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(-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.577778983316170755916793382775478196E-33, -0.529630734706489859590393934210855013E-33), (-0.385185988877447170611195588516985464E-33, +0.168518870133883137142398069976181140E-33), (-0.577778983316170755916793382775478196E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33), (-0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33), (-0.192592994438723585305597794258492732E-33, -0.625927231925851652243192831340101379E-33), (-0.385185988877447170611195588516985464E-33, -0.601853107621011204079993107057789787E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.577778983316170755916793382775478196E-33, -0.818520226364575237548790625598594110E-33), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33), (-0.288889491658085377958396691387739098E-33, -0.770371977754894341222391177033970927E-33)

351reltol = sqrt(epsilon(1._TKC))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, atad(1:size(data)), reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+92

361data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

362data

363+1.79038262, +1.72879899, +1.35045910, +1.87951994, +1.75632453, +1.12272263, +1.90632510, +1.31921721, +1.30731750, +1.72704697, +1.34682035, +1.32585835, +1.26691842, +1.55681491, +1.29800367, +1.57196736, +1.18396354, +1.11461616, +1.35913229, +1.58727074, +1.64299703, +1.90684867, +1.49303222, +1.27605200, +1.89978135, +1.17165053, +1.86199641, +1.20107472, +1.44806981, +1.24759340, +1.57138634, +1.48659384, +1.62913632, +1.10138118, +1.82759285, +1.89451265, +1.24674284, +1.03443110, +1.88221276, +1.09166884, +1.94144261, +1.09694052, +1.97268701, +1.11934543, +1.54818380, +1.32712436, +1.54771423, +1.14576125, +1.13081896, +1.93958116, +1.11433876, +1.03869510, +1.82762468, +1.10009336, +1.04415345, +1.92075062, +1.47079766, +1.47867739, +1.04551101, +1.75195217, +1.99492323, +1.30897677, +1.51328838, +1.22653615, +1.10765707, +1.99550784, +1.94636154, +1.26862609, +1.22243357, +1.57512963, +1.04048371, +1.48964024, +1.10298443, +1.52583122, +1.14875650, +1.47541666, +1.13444936, +1.68237340, +1.34834313, +1.34061599, +1.35742056, +1.69504833, +1.41407883, +1.15701771, +1.77436352, +1.61500537, +1.62239861, +1.56578422, +1.43487144, +1.27857137, +1.65249002, +1.91688895

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.79038262, +1.72879910, +1.35045862, +1.87952018, +1.75632381, +1.12272215, +1.90632439, +1.31921685, +1.30731726, +1.72704697, +1.34681988, +1.32585835, +1.26691806, +1.55681479, +1.29800367, +1.57196724, +1.18396354, +1.11461651, +1.35913193, +1.58727074, +1.64299655, +1.90684855, +1.49303174, +1.27605188, +1.89978087, +1.17165077, +1.86199594, +1.20107508, +1.44806933, +1.24759340, +1.57138574, +1.48659384, +1.62913609, +1.10138106, +1.82759249, +1.89451265, +1.24674237, +1.03443074, +1.88221240, +1.09166837, +1.94144225, +1.09694052, +1.97268665, +1.11934555, +1.54818344, +1.32712436, +1.54771411, +1.14576101, +1.13081884, +1.93958116, +1.11433840, +1.03869534, +1.82762432, +1.10009336, +1.04415333, +1.92075014, +1.47079742, +1.47867727, +1.04551077, +1.75195205, +1.99492288, +1.30897665, +1.51328826, +1.22653604, +1.10765719, +1.99550796, +1.94636130, +1.26862621, +1.22243357, +1.57512951, +1.04048371, +1.48964012, +1.10298443, +1.52583122, +1.14875627, +1.47541666, +1.13444936, +1.68237340, +1.34834337, +1.34061611, +1.35742068, +1.69504845, +1.41407859, +1.15701771, +1.77436352, +1.61500514, +1.62239885, +1.56578386, +1.43487132, +1.27857125, +1.65248966, +1.91688871, +0.238418579E-6, -0.238418579E-6, +0.357627869E-6, +0.119209290E-6, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.298023224E-6, -0.119209290E-6, +0.298023224E-6, +0.00000000, +0.298023224E-6, +0.596046448E-7, +0.119209290E-6, -0.119209290E-6, +0.119209290E-6, -0.596046448E-7, +0.238418579E-6, +0.119209290E-6, +0.476837158E-6, +0.178813934E-6, +0.417232513E-6, -0.596046448E-7, +0.417232513E-6, -0.298023224E-6, +0.238418579E-6, +0.119209290E-6, +0.417232513E-6, +0.357627869E-6, +0.00000000, +0.178813934E-6, +0.119209290E-6, +0.596046448E-7, +0.00000000, -0.178813934E-6, +0.238418579E-6

368reltol = sqrt(epsilon(1._TKC))

369reltol

370+0.345266977E-3

371isClose(data, atad(1:size(data)), reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+22

378data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

379data

380+1.3396077343594079, +1.8043943159446534, +1.8558074450408504, +1.5408191445618944, +1.1742733236070153, +1.1222186296899226, +1.7111085499607455, +1.3662954617182153, +1.3173956251954859, +1.8331041618682704, +1.7937294576556133, +1.1884975994253779, +1.7589559786703337, +1.8122332540195032, +1.2874111993477049, +1.5071596652946415, +1.4105359955409216, +1.2308537008647480, +1.1518179581917611, +1.3099932087992547, +1.8889151257000893, +1.0517025147087506

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.3396077343594077, +1.8043943159446529, +1.8558074450408504, +1.5408191445618948, +1.1742733236070149, +1.1222186296899228, +1.7111085499607450, +1.3662954617182157, +1.3173956251954859, +1.8331041618682702, +1.7937294576556131, +1.1884975994253784, +1.7589559786703339, +1.8122332540195027, +1.2874111993477046, +1.5071596652946413, +1.4105359955409214, +1.2308537008647478, +1.1518179581917605, +1.3099932087992547, +1.8889151257000889, +1.0517025147087502, +0.0000000000000000, -0.44408920985006262E-15, -0.33306690738754696E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.33306690738754696E-15

385reltol = sqrt(epsilon(1._TKC))

386reltol

387+0.14901161193847656E-7

388isClose(data, atad(1:size(data)), reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+40

395data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

396data

397+1.33992648703044685104061222869467961, +1.11442601738917885974580741552076892, +1.08231203473894970529048557879301606, +1.96565021729112807232095503884100219, +1.37619351558106698333152718668589206, +1.52467682434647408335112644265664503, +1.43090636933716870979592631656459355, +1.85567192122136638964628109819300044, +1.60379494293596922587053316608850208, +1.01159638270725264142326168216949422, +1.48095417223247597721487281947366793, +1.23060549321876788861995692965741485, +1.54947650384606119794053285193098081, +1.35721688611658413830593785275202775, +1.62666560030025159509731603568637344, +1.66572247202692276855274989159882954, +1.55044089388281455786924198636599353, +1.25725990771926394802195257406437462, +1.61406264680025333797701585053270496, +1.80707048344746182217843110236449758, +1.82140595632703553894432668578162356, +1.73960246490681862069669411440518242, +1.44682093166552175820490804415056710, +1.22301019145886637033044822522540802, +1.59874360085184621877652131221113481, +1.71664203570642085830257130011267866, +1.13883635719509187991586792996646326, +1.67693899298800660491239153125333857, +1.67256076357567164790557736824568597, +1.77545299239559553395675633457135033, +1.18039628256447033828111503111573189, +1.27674819906958068695949573559055691, +1.24819137693338596596917354852511993, +1.27666507956778509546883423291805749, +1.32075507320319900379415682726716814, +1.69174296072877841623796514305751669, +1.06357362387771362083260261857092987, +1.19780236900014789816407438322556560, +1.97038595742317672748347337688246174, +1.97004584817600861152572451024060770

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.33992648703044685104061222869467961, +1.11442601738917885974580741552076892, +1.08231203473894970529048557879301586, +1.96565021729112807232095503884100181, +1.37619351558106698333152718668589263, +1.52467682434647408335112644265664503, +1.43090636933716870979592631656459374, +1.85567192122136638964628109819300044, +1.60379494293596922587053316608850227, +1.01159638270725264142326168216949422, +1.48095417223247597721487281947366773, +1.23060549321876788861995692965741485, +1.54947650384606119794053285193098120, +1.35721688611658413830593785275202737, +1.62666560030025159509731603568637344, +1.66572247202692276855274989159882935, +1.55044089388281455786924198636599334, +1.25725990771926394802195257406437443, +1.61406264680025333797701585053270496, +1.80707048344746182217843110236449739, +1.82140595632703553894432668578162356, +1.73960246490681862069669411440518223, +1.44682093166552175820490804415056710, +1.22301019145886637033044822522540782, +1.59874360085184621877652131221113481, +1.71664203570642085830257130011267866, +1.13883635719509187991586792996646364, +1.67693899298800660491239153125333838, +1.67256076357567164790557736824568578, +1.77545299239559553395675633457135052, +1.18039628256447033828111503111573151, +1.27674819906958068695949573559055691, +1.24819137693338596596917354852511993, +1.27666507956778509546883423291805749, +1.32075507320319900379415682726716833, +1.69174296072877841623796514305751631, +1.06357362387771362083260261857092968, +1.19780236900014789816407438322556541, +1.97038595742317672748347337688246212, +1.97004584817600861152572451024060770, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, +0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.674075480535532548569592279904724561E-33, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33

402reltol = sqrt(epsilon(1._TKC))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, atad(1:size(data)), reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+56

412data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

413data

414(+1.15828288, +0.392889977E-1), (+1.14713752, +0.545442104), (+1.52093506, +0.666820467), (+1.74176908, +0.880344212), (+1.53740978, +0.680033624), (+1.51774454, +0.153212845), (+1.01441944, +0.540628374), (+1.96076703, +0.142254412), (+1.19369197, +0.753666639), (+1.85579503, +0.535682678), (+1.61709332, +0.327859521), (+1.45514333, +0.775594890), (+1.42546630, +0.501241744), (+1.48383057, +0.723467588), (+1.44585216, +0.179617703), (+1.97017193, +0.602659941), (+1.77517319, +0.819857180), (+1.81578684, +0.103504002), (+1.16385150, +0.713936448), (+1.48698711, +0.906545460), (+1.50547004, +0.627585292), (+1.24637270, +0.371355832), (+1.04805219, +0.288840175), (+1.82501459, +0.817158699), (+1.91038465, +0.349461436), (+1.95777702, +0.748216748), (+1.58891249, +0.915904880), (+1.68179274, +0.105146587), (+1.97348285, +0.375499606), (+1.38141251, +0.812205493), (+1.99857283, +0.904581368), (+1.32370257, +0.438638806), (+1.39295077, +0.197411180), (+1.50123811, +0.771958530), (+1.20268714, +0.246001363), (+1.88695645, +0.737144291), (+1.50429845, +0.384409666), (+1.22221136, +0.266696811E-1), (+1.86209142, +0.553034008), (+1.35587263, +0.892545700), (+1.38715243, +0.807214200), (+1.61164427, +0.913257658), (+1.03056097, +0.631593525), (+1.45663857, +0.307286263), (+1.52267671, +0.532833815), (+1.07907081, +0.161043525), (+1.36292076, +0.533097148), (+1.87142229, +0.843462944), (+1.80306220, +0.907884240), (+1.78973269, +0.587276816E-1), (+1.68358564, +0.105084240), (+1.55066085, +0.916535854), (+1.67556071, +0.995509148), (+1.80626512, +0.704005659), (+1.84052229, +0.399561524), (+1.29132032, +0.944871247)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.15828276, +0.392889753E-1), (+1.14713740, +0.545442224), (+1.52093494, +0.666820407), (+1.74176896, +0.880344272), (+1.53740990, +0.680033505), (+1.51774454, +0.153212845), (+1.01441932, +0.540628314), (+1.96076691, +0.142254353), (+1.19369197, +0.753666580), (+1.85579491, +0.535682797), (+1.61709321, +0.327859640), (+1.45514321, +0.775594950), (+1.42546642, +0.501241744), (+1.48383057, +0.723467767), (+1.44585216, +0.179617852), (+1.97017169, +0.602659881), (+1.77517307, +0.819857240), (+1.81578672, +0.103504054), (+1.16385150, +0.713936448), (+1.48698711, +0.906545341), (+1.50547004, +0.627585232), (+1.24637270, +0.371355891), (+1.04805231, +0.288840115), (+1.82501459, +0.817158759), (+1.91038442, +0.349461496), (+1.95777678, +0.748216689), (+1.58891213, +0.915904760), (+1.68179250, +0.105146781), (+1.97348285, +0.375499666), (+1.38141239, +0.812205434), (+1.99857235, +0.904581308), (+1.32370245, +0.438638806), (+1.39295053, +0.197411150), (+1.50123811, +0.771958470), (+1.20268714, +0.246001378), (+1.88695633, +0.737144232), (+1.50429857, +0.384409606), (+1.22221160, +0.266696736E-1), (+1.86209130, +0.553033948), (+1.35587275, +0.892545700), (+1.38715219, +0.807214200), (+1.61164427, +0.913257480), (+1.03056085, +0.631593466), (+1.45663834, +0.307286471), (+1.52267659, +0.532833636), (+1.07907093, +0.161043584), (+1.36292064, +0.533097029), (+1.87142205, +0.843463004), (+1.80306208, +0.907884240), (+1.78973258, +0.587276891E-1), (+1.68358564, +0.105084151), (+1.55066085, +0.916535795), (+1.67556071, +0.995509088), (+1.80626512, +0.704005599), (+1.84052229, +0.399561465), (+1.29132056, +0.944871128), (+0.596046448E-7, -0.596046448E-7), (+0.655651093E-6, -0.596046448E-7), (+0.357627869E-6, +0.894069672E-7), (+0.476837158E-6, +0.372529030E-6), (+0.298023224E-6, -0.342726707E-6), (+0.238418579E-6, -0.298023224E-7), (+0.238418579E-6, -0.298023224E-7), (+0.238418579E-6, +0.283122063E-6)

419reltol = sqrt(epsilon(1._TKC))

420reltol

421+0.345266977E-3

422isClose(data, atad(1:size(data)), reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+54

429data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

430data

431(+1.3506190718233446, +0.81874220517628071), (+1.5269747836572733, +0.71069769461466614), (+1.7047753304239199, +0.49704577112066839), (+1.3653550119080116, +0.17545426061686809), (+1.8980252680670715, +0.95631055225933481), (+1.2443205497480374, +0.26196777309937525E-1), (+1.2935100091106926, +0.78302430868507766), (+1.2326911063269181, +0.59248161536909716), (+1.3465640341480642, +0.88668869848346177), (+1.4024678814387692, +0.23555888556895177), (+1.4009279541204467, +0.96055710815147588), (+1.2418796239954166, +0.42761400654384851), (+1.7099365082148497, +0.13567952511078407), (+1.5486743176549163, +0.27573171281760411), (+1.1314519172257211, +0.54748557576910095), (+1.5694419201675556, +0.42040248154904736), (+1.4560423082624361, +0.27159050584651223), (+1.4848619739670710, +0.26204602135863608), (+1.1227962013157224, +0.98896868076897348), (+1.7462369219555933, +0.25194687194742460), (+1.5920206277649802, +0.79209146827815557), (+1.5527673801915802, +0.47793868303626974E-1), (+1.2899296201946846, +0.27584712459333971), (+1.3669153030109618, +0.25419694783477653), (+1.3116454520375971, +0.67229544043335332), (+1.1031480390217012, +0.60953931633192637), (+1.3828663111029624, +0.88323706487487386), (+1.2351769654372258, +0.49732743400347801), (+1.0664142111009673, +0.36861711568226718), (+1.7612804287747124, +0.30259797593995719), (+1.1178623804993331, +0.57114860124283562), (+1.1491085962621224, +0.60570535623824051), (+1.6416676205822376, +0.54140424463373638), (+1.7265739092516346, +0.66587527214394182), (+1.4834961323146039, +0.43869536649608032), (+1.0148696521773322, +0.76318211115853174), (+1.0615645241880807, +0.67921724587656007), (+1.2549066069953767, +0.11068528574286762), (+1.2114468589517768, +0.44009103039774877), (+1.8484320601144679, +0.42921683212998585), (+1.0192836403552863, +0.51175825755521975), (+1.4135577904032108, +0.86779374270197074), (+1.7562229088034191, +0.48473117385304176), (+1.7566681921954928, +0.78844782405888714), (+1.4166990290937318, +0.35358114717734734), (+1.5897601672312907, +0.60663951454142262), (+1.4121507489133065, +0.61744024459888058), (+1.9788169757017808, +0.47940920176238855E-1), (+1.4711613492590256, +0.37398019529594639), (+1.8864917659576705, +0.69275415380220751E-1), (+1.4716585140956091, +0.19437985211803122), (+1.6833014475234154, +0.92652943465795046), (+1.0008379610867228, +0.36789564876116065), (+1.8348310746582421, +0.50697517986926632)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.3506190718233444, +0.81874220517628093), (+1.5269747836572738, +0.71069769461466614), (+1.7047753304239197, +0.49704577112066856), (+1.3653550119080116, +0.17545426061686797), (+1.8980252680670717, +0.95631055225933492), (+1.2443205497480379, +0.26196777309937448E-1), (+1.2935100091106924, +0.78302430868507755), (+1.2326911063269184, +0.59248161536909705), (+1.3465640341480640, +0.88668869848346188), (+1.4024678814387692, +0.23555888556895210), (+1.4009279541204460, +0.96055710815147577), (+1.2418796239954166, +0.42761400654384873), (+1.7099365082148497, +0.13567952511078429), (+1.5486743176549165, +0.27573171281760445), (+1.1314519172257209, +0.54748557576910128), (+1.5694419201675556, +0.42040248154904786), (+1.4560423082624361, +0.27159050584651234), (+1.4848619739670714, +0.26204602135863614), (+1.1227962013157229, +0.98896868076897348), (+1.7462369219555933, +0.25194687194742482), (+1.5920206277649804, +0.79209146827815546), (+1.5527673801915802, +0.47793868303627057E-1), (+1.2899296201946846, +0.27584712459333971), (+1.3669153030109622, +0.25419694783477653), (+1.3116454520375971, +0.67229544043335321), (+1.1031480390217014, +0.60953931633192626), (+1.3828663111029624, +0.88323706487487352), (+1.2351769654372264, +0.49732743400347779), (+1.0664142111009676, +0.36861711568226696), (+1.7612804287747121, +0.30259797593995719), (+1.1178623804993335, +0.57114860124283551), (+1.1491085962621232, +0.60570535623824040), (+1.6416676205822374, +0.54140424463373638), (+1.7265739092516346, +0.66587527214394204), (+1.4834961323146041, +0.43869536649608026), (+1.0148696521773326, +0.76318211115853163), (+1.0615645241880811, +0.67921724587655996), (+1.2549066069953771, +0.11068528574286760), (+1.2114468589517766, +0.44009103039774866), (+1.8484320601144684, +0.42921683212998590), (+1.0192836403552861, +0.51175825755521953), (+1.4135577904032108, +0.86779374270197041), (+1.7562229088034185, +0.48473117385304165), (+1.7566681921954928, +0.78844782405888680), (+1.4166990290937318, +0.35358114717734729), (+1.5897601672312904, +0.60663951454142229), (+1.4121507489133061, +0.61744024459888047), (+1.9788169757017811, +0.47940920176238910E-1), (+1.4711613492590256, +0.37398019529594639), (+1.8864917659576705, +0.69275415380220792E-1), (+1.4716585140956093, +0.19437985211803094), (+1.6833014475234158, +0.92652943465795035), (+1.0008379610867231, +0.36789564876116060), (+1.8348310746582421, +0.50697517986926643), (+0.22204460492503131E-15, +0.24980018054066022E-15), (+0.44408920985006262E-15, +0.0000000000000000), (+0.0000000000000000, +0.27755575615628914E-15), (+0.55511151231257827E-15, -0.16653345369377348E-15), (+0.44408920985006262E-15, +0.44408920985006262E-15), (+0.11102230246251565E-14, +0.19428902930940239E-15), (+0.66613381477509392E-15, -0.55511151231257827E-16), (+0.66613381477509392E-15, -0.19428902930940239E-15), (+0.11102230246251565E-15, +0.55511151231257827E-15), (+0.99920072216264089E-15, +0.0000000000000000)

436reltol = sqrt(epsilon(1._TKC))

437reltol

438+0.14901161193847656E-7

439isClose(data, atad(1:size(data)), reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+52

446data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

447data

448(+1.88264671081304446129276841369668605, +0.271489929108855256958146302296774287), (+1.29825775481894814289691275711136964, +0.823014894475924533962789195733058929), (+1.17883890449644065160208377144756407, +0.931689278233793290911616967315034034), (+1.25812357479441577452217258026689893, +0.334967060250623307007869956909156318), (+1.23302632011991072029458959915020936, +0.599669584002144606256784776472670743), (+1.87063558312745659996777069126609341, +0.629131469290463899817834113041712569), (+1.18301311290574587416278150893373341, +0.911984194073014631412198120139405634), (+1.05816882483277685564716629155700650, +0.423818321185060613914403219640457936), (+1.30731143664965889673737595077885282, +0.707112723412819422776878530220624309), (+1.95788604085006389735548472313893899, +0.446644783206318096743549608850538685), (+1.01072311529791304801808529132229801, +0.787801267317563150377073996771834780), (+1.85622299126461167577131707873439747, +0.581090010243146053068761638453054455), (+1.01944600200902328405141478479004910, +0.509283347736327590965343910811314000), (+1.82913997779046708424560610869224219, +0.753975881482800655837035053468307260), (+1.66230449970616493497355972485538599, +0.746817541271745260355464412093106605), (+1.16522051453690134950457951895481071, +0.380891306496440150161923417145333734), (+1.64368771165706317311262628145112598, +0.253130356012154021666656876140596530), (+1.44620026878740712292574463364371181, +0.236139404079968793614369785502248754), (+1.47428670431711542687795216566729101, +0.830621288299311392278380933980409222E-1), (+1.70115766055815386305560222432549517, +0.223994174224596038881104251974582960), (+1.21047375985284126114979661500480399, +0.145210357695005914997535787144052493E-1), (+1.88364808760070476697817292582428448, +0.433496780226455409928717681595385967), (+1.16678920335286334808009042304332222, +0.732901715361935120361276749844161092), (+1.61947181069911928381255964983853933, +0.229083174323564936449444842915795421), (+1.78828635669309917129478612170398164, +0.921951356134497608536556453758551172), (+1.17064933726057787341577558173497209, +0.560888955062475624908383862697138115), (+1.74063565727529267799657899448151391, +0.508203040585255694320776645431759584), (+1.20061875856890864488679067377355289, +0.783188066458595053520327983275104697), (+1.48573055237419806170770528263502701, +0.646317437043761950756885664634048804), (+1.06194317196773544238988225754029178, +0.605324569703183933242539554706680353), (+1.24906046912319775025786868824237442, +0.771845396085897628646470804110959294), (+1.51508658402735993469644601240549754, +0.428609160852167387357163532198243502), (+1.64798243433431961024125894892054427, +0.394336070747589309277310342119694634E-1), (+1.73255290407087915580533580242886766, +0.241934843867248538954615452627734563), (+1.76766822377844972519405112019455264, +0.532096648627771267478093502865620789), (+1.84280494138081868434064210749017138, +0.750574101906497881199308956289241968E-1), (+1.30177842068925915349735603606210747, +0.423149644288680943431937910456734399), (+1.10806432674489838554295219714807295, +0.825015512483111447557522141959655579), (+1.88439563815381727081280172149559891, +0.100637483025007934496447395781538197), (+1.99924449902509239458937621692564011, +0.198777737650654532368531532366818030), (+1.84399533460072363572947909718161382, +0.230081011495694751906763407508396349), (+1.82125474491852428633471571601371251, +0.278988441318723389939453992136774191), (+1.30046726164444695523223351031651224, +0.446318764063260835264335196624870612), (+1.55586458377947155191174788903648560, +0.508462586368702576420232523486866006), (+1.85999646160712958824110258008145438, +0.479770749853068022268739365815137095), (+1.49011533210529613469023630604944324, +0.256466630768769987658083409815875125), (+1.50670432829758509378666601433994099, +0.571216944344628838826127713497340802), (+1.58920007023133179622032116225032024, +0.246820121820508544346417228187783377), (+1.82543111564587486424187060039764991, +0.689742530842425833446435311010301384), (+1.78239132629437636420658325446739508, +0.282325584031954220053115044591289137), (+1.13540003450507006966971666854634098, +0.397417372677990899305734715277918921), (+1.60250226017013349169253443033083607, +0.151310200886394044969192448969225540)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.88264671081304446129276841369668605, +0.271489929108855256958146302296774384), (+1.29825775481894814289691275711136964, +0.823014894475924533962789195733059025), (+1.17883890449644065160208377144756427, +0.931689278233793290911616967315034130), (+1.25812357479441577452217258026689874, +0.334967060250623307007869956909156366), (+1.23302632011991072029458959915020956, +0.599669584002144606256784776472670839), (+1.87063558312745659996777069126609379, +0.629131469290463899817834113041712473), (+1.18301311290574587416278150893373322, +0.911984194073014631412198120139405538), (+1.05816882483277685564716629155700630, +0.423818321185060613914403219640457839), (+1.30731143664965889673737595077885263, +0.707112723412819422776878530220624309), (+1.95788604085006389735548472313893899, +0.446644783206318096743549608850538878), (+1.01072311529791304801808529132229839, +0.787801267317563150377073996771834973), (+1.85622299126461167577131707873439728, +0.581090010243146053068761638453054647), (+1.01944600200902328405141478479004910, +0.509283347736327590965343910811314096), (+1.82913997779046708424560610869224238, +0.753975881482800655837035053468307260), (+1.66230449970616493497355972485538599, +0.746817541271745260355464412093106701), (+1.16522051453690134950457951895481032, +0.380891306496440150161923417145333590), (+1.64368771165706317311262628145112579, +0.253130356012154021666656876140596626), (+1.44620026878740712292574463364371200, +0.236139404079968793614369785502248730), (+1.47428670431711542687795216566729101, +0.830621288299311392278380933980408260E-1), (+1.70115766055815386305560222432549517, +0.223994174224596038881104251974582936), (+1.21047375985284126114979661500480399, +0.145210357695005914997535787144050567E-1), (+1.88364808760070476697817292582428448, +0.433496780226455409928717681595385870), (+1.16678920335286334808009042304332222, +0.732901715361935120361276749844161285), (+1.61947181069911928381255964983853952, +0.229083174323564936449444842915795181), (+1.78828635669309917129478612170398164, +0.921951356134497608536556453758551172), (+1.17064933726057787341577558173497209, +0.560888955062475624908383862697137923), (+1.74063565727529267799657899448151410, +0.508203040585255694320776645431759488), (+1.20061875856890864488679067377355270, +0.783188066458595053520327983275104697), (+1.48573055237419806170770528263502701, +0.646317437043761950756885664634048804), (+1.06194317196773544238988225754029217, +0.605324569703183933242539554706680257), (+1.24906046912319775025786868824237442, +0.771845396085897628646470804110959294), (+1.51508658402735993469644601240549754, +0.428609160852167387357163532198243502), (+1.64798243433431961024125894892054427, +0.394336070747589309277310342119695838E-1), (+1.73255290407087915580533580242886785, +0.241934843867248538954615452627734707), (+1.76766822377844972519405112019455283, +0.532096648627771267478093502865620886), (+1.84280494138081868434064210749017138, +0.750574101906497881199308956289242450E-1), (+1.30177842068925915349735603606210766, +0.423149644288680943431937910456734496), (+1.10806432674489838554295219714807257, +0.825015512483111447557522141959655676), (+1.88439563815381727081280172149559891, +0.100637483025007934496447395781538197), (+1.99924449902509239458937621692564011, +0.198777737650654532368531532366817909), (+1.84399533460072363572947909718161362, +0.230081011495694751906763407508396446), (+1.82125474491852428633471571601371251, +0.278988441318723389939453992136774191), (+1.30046726164444695523223351031651224, +0.446318764063260835264335196624870515), (+1.55586458377947155191174788903648541, +0.508462586368702576420232523486865910), (+1.85999646160712958824110258008145438, +0.479770749853068022268739365815137432), (+1.49011533210529613469023630604944305, +0.256466630768769987658083409815875029), (+1.50670432829758509378666601433994119, +0.571216944344628838826127713497340898), (+1.58920007023133179622032116225032024, +0.246820121820508544346417228187783714), (+1.82543111564587486424187060039764971, +0.689742530842425833446435311010301577), (+1.78239132629437636420658325446739527, +0.282325584031954220053115044591289089), (+1.13540003450507006966971666854634117, +0.397417372677990899305734715277918921), (+1.60250226017013349169253443033083607, +0.151310200886394044969192448969225372), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (+0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33), (+0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, -0.529630734706489859590393934210855013E-33), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.722223729145213444895991728469347744E-34)

453reltol = sqrt(epsilon(1._TKC))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, atad(1:size(data)), reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+38

463data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

464data

465+1.18663931, +1.76260269, +1.57526088, +1.75525904, +1.99418664, +1.28215671, +1.73010373, +1.70699298, +1.49907708, +1.99025714, +1.30063426, +1.83425748, +1.41724002, +1.47083664, +1.20561886, +1.77094710, +1.44134998, +1.64351463, +1.22286630, +1.94446993, +1.66575837, +1.13719153, +1.49922192, +1.32963204, +1.65468693, +1.79888988, +1.59880447, +1.91134238, +1.13477445, +1.26534855, +1.42714572, +1.54954362, +1.75051904, +1.94929075, +1.51934421, +1.67688537, +1.35684824, +1.02564883

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.18663931, +1.76260257, +1.57526064, +1.75525868, +1.99418652, +1.28215647, +1.73010373, +1.70699263, +1.49907672, +1.99025691, +1.30063415, +1.83425725, +1.41723990, +1.47083664, +1.20561886, +1.77094698, +1.44135010, +1.64351439, +1.22286654, +1.94446969, +1.66575837, +1.13719153, +1.49922204, +1.32963204, +1.65468693, +1.79888976, +1.59880447, +1.91134214, +1.13477433, +1.26534843, +1.42714572, +1.54954350, +1.75051928, +1.94929075, +1.51934433, +1.67688525, +1.35684836, +1.02564859, -0.596046448E-7, +0.596046448E-7, +0.357627869E-6, -0.119209290E-6, +0.178813934E-6, +0.119209290E-6, +0.298023224E-6, -0.178813934E-6, -0.596046448E-7, +0.596046448E-7, +0.00000000, -0.596046448E-7, -0.596046448E-7, +0.00000000, +0.00000000, -0.596046448E-7, -0.596046448E-7, -0.119209290E-6, +0.00000000, -0.119209290E-6, +0.596046448E-7, -0.596046448E-7, +0.119209290E-6, -0.596046448E-7, -0.596046448E-7, +0.00000000

470reltol = sqrt(epsilon(1._TKC))

471reltol

472+0.345266977E-3

473isClose(data, atad(1:size(data)), reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+72

480data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

481data

482+1.8599150294891706, +1.7361339129533448, +1.2633503353367330, +1.8356672556999163, +1.5014810649714030, +1.6522719550184941, +1.2193918597341566, +1.0149415585798083, +1.9121770440958927, +1.3530044875728262, +1.4183677609928869, +1.1652542319887316, +1.7298175121273269, +1.9281475587323431, +1.7276301704154151, +1.4576316388322548, +1.3955710683537692, +1.1525438667732464, +1.7569003428845833, +1.0660237975565998, +1.5521422695741625, +1.4218899616848386, +1.8614834184684441, +1.0949105389788021, +1.2567837895971272, +1.6192760613424824, +1.0901581269100908, +1.7313656805862110, +1.1187204788609435, +1.2140273749065256, +1.5309597811300022, +1.8602221750432451, +1.9557347995123808, +1.7840286704898560, +1.5598695144013703, +1.8471208236002452, +1.1575630029830730, +1.7398636992888785, +1.4055325507662526, +1.5266880192927998, +1.6524527812997480, +1.3308795198265435, +1.7587671207203823, +1.7750745434271109, +1.8980117422485956, +1.8360702868240815, +1.5576843839568966, +1.3671490371288364, +1.3784265604376396, +1.0855188743020610, +1.4141412999179221, +1.7975475340934302, +1.0209399510327106, +1.2403258513565634, +1.9381909093407625, +1.3168435172781259, +1.5671171486926578, +1.2551559745044001, +1.2931212125514377, +1.5282609757775489, +1.8430154762533415, +1.8669280620996005, +1.9117111326040774, +1.8940837783355038, +1.9043337391412276, +1.9874941979286205, +1.8994895219787615, +1.6246624177678941, +1.4471410904015785, +1.2275401339037801, +1.5217035378075146, +1.1471846645852311

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.8599150294891704, +1.7361339129533451, +1.2633503353367328, +1.8356672556999165, +1.5014810649714019, +1.6522719550184939, +1.2193918597341560, +1.0149415585798078, +1.9121770440958925, +1.3530044875728267, +1.4183677609928869, +1.1652542319887318, +1.7298175121273267, +1.9281475587323431, +1.7276301704154147, +1.4576316388322548, +1.3955710683537690, +1.1525438667732466, +1.7569003428845833, +1.0660237975566003, +1.5521422695741620, +1.4218899616848386, +1.8614834184684432, +1.0949105389788021, +1.2567837895971266, +1.6192760613424828, +1.0901581269100904, +1.7313656805862112, +1.1187204788609428, +1.2140273749065256, +1.5309597811300018, +1.8602221750432451, +1.9557347995123808, +1.7840286704898558, +1.5598695144013708, +1.8471208236002450, +1.1575630029830730, +1.7398636992888779, +1.4055325507662531, +1.5266880192927998, +1.6524527812997480, +1.3308795198265435, +1.7587671207203823, +1.7750745434271109, +1.8980117422485956, +1.8360702868240808, +1.5576843839568966, +1.3671490371288366, +1.3784265604376396, +1.0855188743020607, +1.4141412999179221, +1.7975475340934302, +1.0209399510327106, +1.2403258513565627, +1.9381909093407623, +1.3168435172781252, +1.5671171486926574, +1.2551559745043996, +1.2931212125514375, +1.5282609757775485, +1.8430154762533411, +1.8669280620995994, +1.9117111326040774, +1.8940837783355033, +1.9043337391412274, +1.9874941979286205, +1.8994895219787613, +1.6246624177678941, +1.4471410904015787, +1.2275401339037795, +1.5217035378075148, +1.1471846645852304, -0.33306690738754696E-15, -0.22204460492503131E-15, -0.44408920985006262E-15, -0.55511151231257827E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, -0.44408920985006262E-15, -0.22204460492503131E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.33306690738754696E-15, +0.33306690738754696E-15, +0.0000000000000000, +0.77715611723760958E-15, +0.0000000000000000, +0.0000000000000000, -0.33306690738754696E-15, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, -0.55511151231257827E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.33306690738754696E-15, -0.22204460492503131E-15, -0.11102230246251565E-15, +0.22204460492503131E-15, -0.44408920985006262E-15, -0.11102230246251565E-15, -0.44408920985006262E-15, +0.0000000000000000, -0.44408920985006262E-15, +0.0000000000000000, -0.66613381477509392E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, -0.22204460492503131E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.22204460492503131E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.44408920985006262E-15, +0.99920072216264089E-15, -0.33306690738754696E-15, +0.44408920985006262E-15

487reltol = sqrt(epsilon(1._TKC))

488reltol

489+0.14901161193847656E-7

490isClose(data, atad(1:size(data)), reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+22

497data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

498data

499+1.12194237149176814136612815766971556, +1.54846754047384801427135360226899049, +1.63549895932122161474863706026095118, +1.04001658464038776457935524868415527, +1.09105344540884943805896425839629857, +1.45801556419598049844512039340352652, +1.13706539811518224752621750692862156, +1.56601070127836876643174252975983431, +1.44219338782241841700575325211229879, +1.57983126623925703055919566385957932, +1.27157666163901722823286090417211960, +1.33743280519286013693159576774016748, +1.74933986229349330901367354616320775, +1.38114419765251258076250463562432904, +1.16362097921640976745607042829053232, +1.41037966624392646588018465558173076, +1.53351151710694029981777340730187025, +1.26890980616284438166408287204935238, +1.33478355661132531889308774262431742, +1.87634796370881396768600410256830852, +1.72755678667712682840066413594333834, +1.21081301323145914443791515840034157

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.12194237149176814136612815766971537, +1.54846754047384801427135360226899049, +1.63549895932122161474863706026095156, +1.04001658464038776457935524868415546, +1.09105344540884943805896425839629857, +1.45801556419598049844512039340352671, +1.13706539811518224752621750692862176, +1.56601070127836876643174252975983450, +1.44219338782241841700575325211229898, +1.57983126623925703055919566385957932, +1.27157666163901722823286090417211998, +1.33743280519286013693159576774016748, +1.74933986229349330901367354616320852, +1.38114419765251258076250463562432924, +1.16362097921640976745607042829053270, +1.41037966624392646588018465558173076, +1.53351151710694029981777340730187044, +1.26890980616284438166408287204935257, +1.33478355661132531889308774262431742, +1.87634796370881396768600410256830871, +1.72755678667712682840066413594333873, +1.21081301323145914443791515840034157, -0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33

504reltol = sqrt(epsilon(1._TKC))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, atad(1:size(data)), reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

510

511

Test:: test_pm_fftnr

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, you must acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library, you must also ask the end users to cite this original ParaMonte library.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 428 of file pm_fftnr.F90.

The documentation for this interface was generated from the following file:

/home/amir/git/paramonte/src/fortran/main/pm_fftnr.F90